Payoff dominance, a criterion for choosing between equilibrium points in games, is intuitively compelling, especially in matching games and other games of common interests, but it has not been justified from standard game-theoretic rationality assumptions. A psychological explanation of it is offered in terms of a form of reasoning that we call the Stackelberg heuristic in which players assume that their strategic thinking will be anticipated by their co-player(s). Two-person games are called Stackelberg-soluble if the players' strategies that maximize against (...) their co-players' best replies intersect in a Nash equilibrium. Proofs are given that every game of common interests is Stackelberg-soluble, that a Stackelberg solution is always a payoff-dominant outcome, and that in every game with multiple Nash equilibria a Stackelberg solution is a payoff-dominant equilibrium point. It is argued that the Stackelberg heuristic may be justified by evidentialist reasoning. (shrink)

Virtual bargaining theory suggests that social agents aim to resolve non-cooperative games by identifying the strategy profile which they would agree to play if they could openly bargain. The theory thus offers an explanation of how social agents resolve games with multiple Nash equilibria. One of the main questions pertaining to this theory is how the principles of the bargaining theory could be applied in the analysis of hypothetical bargaining in non-cooperative games. I propose a bargaining model (...) based on the benefit-equilibrating bargaining solution concept for non-cooperative games, broadly in line with the principles underlying Conley and Wilkie's ordinal egalitarian solution for Pareto optimal point selection problems with finite choice sets. I provide formal characterizations of the ordinal and the cardinal versions of BES, discuss their application to n-player games, and compare model's theoretical predictions with the data available from several experiments involving `pie games'. (shrink)

Various potential strategic interactions between a “strong” Artificial intelligence and humans are analyzed using simple 2 × 2 order games, drawing on the New Periodic Table of those games developed by Robinson and Goforth. Strong risk aversion on the part of the human player leads to shutting down the AI research program, but alternative preference orderings by the human and the AI result in Nash equilibria with interesting properties. Some of the AI-Human games have multiple equilibria, (...) and in other cases Pareto-improvement over the Nash equilibrium could be attained if the AI’s behavior towards humans could be guaranteed to be benign. The preferences of a superintelligent AI cannot be known in advance, but speculation is possible as to its ranking of alternative states of the world, and how it might assimilate the accumulated wisdom of humanity. (shrink)

In this paper we describe an argumentation-based representation of normal form games, and demonstrate how argumentation can be used to compute pure strategy Nash equilibria. Our approach builds on Modgil’s Extended Argumentation Frameworks. We demonstrate its correctness, showprove several theoretical properties it satisfies, and outline how it can be used to explain why certain strategies are Nash equilibria to a non-expert human user.

We study experimentally a coordination game with N heterogeneous individuals under different information treatments. We explore the effects of information on the emergence of Pareto-efficient outcomes, by means of a gradual decrease of the information content provided to the players in successive experiments. We observe that successful coordination is possible with private information alone, although not on a Pareto-optimal equilibrium. Reinforcement-based learning models reproduce the qualitative trends of the experimental results.

Here, we present some experiments of non-cooperative games of network formation based on Bala and Goyal (Econometrica 68:1181–1229, 2000 ). We have looked at the one-way and the two-way flow models, each for high and low link costs. The models come up with both multiple equilibria and coordination problems. We conducted the experiments under various conditions which allowed for repeated interactions between subjects. We found that coordination on non-empty Strict Nash equilibria was not an easy task (...) to achieve, even in the one-way model where the Strict Nash equilibria are wheels. We found some evidence of convergence to equilibrium networks through learning dynamics, while we found no effect of salient labels to help coordination. The evidence on learning behavior provides support for subjects that were choosing strategies in line with various learning rules, principally Reinforcement and Fictitious Play. (shrink)

The article studies properties of interchangeability of pure, mixed, strict, and strict mixed Nash equilibria. The main result is a sound and complete axiomatic system that describes properties of interchangeability in all four settings. It has been previously shown that the same axiomatic system also describes properties of independence in probability theory, nondeducibility in information flow, and non-interference in concurrency theory.

Nash Equilibrium is a central concept ingame theory. It has been argued that playing NashEquilibrium strategies is rational advice for agentsinvolved in one-time strategic interactions capturedby non-cooperative game theory. This essaydiscusses arguments for that position: vonNeumann–Morgenstern's argument for their minimaxsolution, the argument from self-enforcingagreements, the argument from the absence ofprobabilities, the transparency-of-reasons argument,the argument from regret, and the argument fromcorrelated equilibrium. All of these argumentseither fail entirely or have a very limited scope.Whatever the use of Nash Equilibrium is, (...) therefore,it is not useful as a rational recommendation inone-time strategic interactions. This is good newsfor Bayesians: although this discussion does notargue directly for the Bayesian idea of rationalityas expected utility maximization, it argues againsta position that has been regarded as a contender insituations of strategic interaction. (shrink)

We modify the payment rule of the standard divide the dollar (DD) game by introducing a second stage and thereby resolve the multiplicity problem and implement equal division of the dollar in equilibrium. In the standard DD game, if the sum of players’ demands is less than or equal to a dollar, each player receives what he demanded; if the sum of demands is greater than a dollar, all players receive zero. We modify this second part, which involves a harsh (...) punishment. In the modified game $(D\!D^{\prime })$ , if the demands are incompatible, then players have one more chance. In particular, they play an ultimatum game to avoid the excess. In the two-player version of this game, there is a unique subgame perfect Nash equilibrium in which players demand (and receive) an equal share of the dollar. We also provide an $n$ -player extension of our mechanism. Finally, the mechanism we propose eliminates not only all pure strategy equilibria involving unequal divisions of the dollar, but also all equilibria where players mix over different demands in the first stage. (shrink)

Responding to serious environmental problems, requires urgent and fundamental shifts in our day-to-day lifestyles. This paper employs a qualitative, cross-cultural approach to explore people’s subjective self-reflections on their experiences of pro-environmental behavioral spillover in three countries; Brazil, China, and Denmark. Behavioral spillover is an appealing yet elusive phenomenon, but offers a potential way of encouraging wider, voluntary lifestyle shifts beyond the scope of single behavior change interventions. Behavioral spillover theory proposes that engaging in one pro-environmental action can catalyze the performance (...) of others. To date, evidence for the phenomenon has been mixed, and the causal processes governing relationships between behaviors appear complex, inconsistent and only partly understood. This paper addresses a gap in the literature by investigating accounts of behavioral spillover in three diverse cultural settings using qualitative semi-structured interviews. The analysis shows that while around half of participants overall who were questioned recalled spillover effects, the other half had not consciously experienced spillover. There were few significant differences across cultures, though some forms of spillover effects were reported more in some cultures than others. More environmentally-engaged participants across all three countries were significantly more likely to experience spillover than those who were less engaged. Accounts of within-domain spillovers were most commonly reported, mainly comprising waste, resource conservation and consumption-related actions. Accounts of between-domain spillover were very rare. Recollection of contextual and interpersonal spillover effects also emerged from the interviews. Our findings suggest that more conscious behavioral spillover pathways may be limited to those with pre-existing environmental values. Behavioral spillover may comprise multiple pathways incorporating conscious and unconscious processes. We conclude that targeting behavioral catalysts that generate more socially diffuse spillover effects could offer more potential than conventional spillover involving a single individual. (shrink)

With the rise of ‘globesity’, fat activism and Fat Studies have become political players in countering negative stereotypes and the devaluation of fat bodies. Both groups are diverse, yet share a common goal to celebrate and/or accept fatness, and challenge practices and discourses that reinforce ‘normal’ bodies (such as diets, ‘fat talk’ and medicalisation). In this article, we reflect on our engagement with a Fat Studies conference, and critically interrogate the assumptions that underlie this particular space. It is not surprising (...) that fat activists and Fat Studies scholars bring different ideologies to the table, yet the differences between them have not been adequately scrutinised or theorised. Drawing upon Linda Alcoff’s feminist philosophy, we examine how identity politics and intersectional perspectives are both used in fat activism, yet have the effect of creating unresolved tensions between singular and multiple embodied identities. We argue that an identity politics approach (exemplified through embodied visibility and declarations of ‘thin privilege’) has the potential to create boundaries for policing and exclusion, and is thus at odds with the much broader axes identified by intersectorial approaches. Rather than dismiss the power of identity politics, we argue for a careful reframing of the relationship between identity politics and intersectionality in fat activism and Fat Studies. We suggest that unexamined contradictions that arise from this mismatch may be counterproductive to the important subversive aims of the movement. (shrink)

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash’s best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both (...) types of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return. (shrink)

This article analyzes rent seeking with multiple additive efforts for each of two players. Impact on rent seeking occurs even when a player exerts only one effort. This contrasts with models of multiplicative efforts with impact on rent seeking only when a player exerts all its available efforts. An analytical solution is developed when the contest intensities are below one, and equal to one for one effort. Then, additional efforts causing interior solutions give players higher expected utilities and lower (...) rent dissipation, which contrasts with earlier findings for multiplicative efforts. Players cut back on the effort with contest intensity equal to one, and exert alternative efforts instead. Accounting for solutions which have to be determined numerically, a Nash equilibrium selection method is provided. For illustration, an example with maximum two efforts for each player is provided. Equilibria are shown where both players choose both efforts, or one player withdraws from its most costly effort. Both players may collectively prefer to exclude one of their efforts, though in equilibrium, they may prefer both efforts. When all contest intensities are equal to one or larger than one, only the one most cost-effective effort is exerted, due to the logic of linear or convex production. Rent dissipation increases in the contest intensity, and is maximum when the players are equally advantaged determined by unit effort cost divided by impact. (shrink)

In this article, I analyze the circumstances of justice, that is, the background conditions that are necessary and sufficient for justice to exist between individual parties in society. Contemporary political philosophers almost unanimously accept an account of these circumstances attributed to David Hume. I argue that the conditions of this standard account are neither sufficient nor necessary conditions for justice. In particular, I contend that both a Hobbesian state of nature and a prisoner’s dilemma are cases in which the conditions (...) of the standard account obtain and yet no justice exists between parties. I propose an alternative set of generic circumstances of justice motivated by examples from game theory. Parties are in these generic circumstances with respect to each other when: (1) they are engaged in a conflictual coordination game with multiple strict Nash equilibrium points where, at any of these equilibria, some parties do not receive their greatest payoffs, and (2) they have common knowledge that each party is rational and follows her end of a strict equilibrium where no party receives her greatest payoff. These two conditions reflect the idea that justice requires all parties to make some sacrifices so that others can have more of the goods they need and want. I argue that these generic circumstances are necessary and sufficient conditions for parties to follow generic norms of justice, that is, mutually beneficial practices that require some sacrifices. Key Words: common knowledge • conflictual coordination • correlated equilibrium • moderate selfishness • moderate variable scarcity • rough equality. (shrink)

Growing opioid misuse in the United States has resulted in more children living with an adult with an opioid use history. Although an abundance of research has demonstrated a link between opioid misuse and negative parenting behaviors, few intervention efforts have been made to target this underserved population. The Family Check-Up has been tested in more than 25 years of research, across multiple settings, and is an evidence-based program for reducing risk behavior, enhancing parenting skills, and preventing the onset (...) of substance use. It is designed to motivate parents to engage in positive parenting practices and to change problematic parenting and has been tested across a variety of ages including early childhood and adolescence. It is highlighted in NIDA’s Principles of Substance Use Prevention for Early Childhood: A research-based guide as one of only three effective selective prevention programs for substance abuse among families with young children. Recently, we developed an online version of the FCU that has now been adapted for early childhood and families with opioid use histories. The online platform and telehealth model allow for wide-scale dissemination, ease of training with community providers, and increased public health reach for families in remote, rural areas. This is particularly important when targeting families with opioid misuse and addiction because there are high rates of addiction in remote areas, yet few services available. In this article, we describe the FCU Online and review new content in the model that targets a population of young adult parents with substance abuse histories, including opioid use. New modules include content focused on harm reduction for this high-risk population of parents, such as safety in the home, substance use while parenting, and managing conflict with partners and friends. (shrink)

Large increases unofficial economies in many transition economies arise from a dynamic interaction with rising income inequality and public sector changes in multiple equilibria system. Returns to unofficial activity are first increasing and then decreasing, implying two distinct stable equilibria, with changes in inequality possibly causing a jump from one to the other. Multiple regressions of data from 18 transition economies find income inequality significantly correlated with the size of the unofficial economy, with the maximum annual (...) rate of inflation also significantly correlated. The latter appears to be the only significant correlate with the increase in the size of the unofficial economy. (shrink)

Inspired by Shalev’s model of loss aversion, we investigate the effect of loss aversion on a bimatrix game where the payoffs in the bimatrix game are characterized by triangular fuzzy variables. First, we define three solution concepts of credibilistic loss aversion Nash equilibria, and their existence theorems are presented. Then, three sufficient and necessary conditions are given to find the credibilistic loss aversion Nash equilibria. Moreover, the relationship among the three credibilistic loss aversion Nash (...) class='Hi'>equilibria is discussed in detail. Finally, for2×2bimatix game with triangular fuzzy payoffs, we investigate the effect of loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria. It is found that an increase of loss aversion levels of a player leads to a decrease of his/her own payoff. We also find that the equilibrium utilities of players are decreasing as their own confidence levels when players employ the optimistic value criterion. (shrink)

A strategic equilibrium is a profile of strategies that are each self-supporting given the profile. Strategic equilibria exist in games without Nash equilibria.

Strong Nash equilibrium and coalition-proof Nash equilibrium rely on the idea that players are allowed to form coalitions and make joint deviations. Both of these notions consider cases in which any coalition can be formed. Accordingly, there may arise “conflicts of interest” that prevent a player from choosing an action that simultaneously meets the requirements of two coalitions to which he or she belongs. Here, we address this observation by studying an organizational framework such that the coalitional structure (...) is motivated by real-life examples where players cannot form some coalitions and formulated in such a way that no conflicts of interest remain. We define an organization as an ordered collection of partitions of the player set such that any partition is coarser than the partitions that precede it. For any given organization, we introduce the notion of organizational Nash equilibrium. We analyze the existence of equilibrium in a subclass of games with strategic complementarities and illustrate how the proposed notion refines the set of Nash equilibria in some examples of normal form games. (shrink)

Axelord’s [(1970), Conflict of Interest, Markham Publishers, Chicago] index of conflict in 2 × 2 games with two pure strategy equilibria has the property that a reduction in the cost of holding out corresponds to an increase in conflict. This article takes the opposite view, arguing that if losing becomes less costly, a player is less likely to gamble to win, which means that conflict will be less frequent. This approach leads to a new power index and a new (...) measure of stubbornness, both anchored in strategic reasoning. The win probability defined as power constitutes an equilibrium refinement which differs from Harsanyi and Selten’s [(1988), A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge] refinement. In contrast, Axelrod’s approach focuses on preferences regarding divergences from imaginary outmost rewards that cannot be obtained jointly. The player who is less powerful in an asymmetric one-shot game becomes more powerful in the repeated game, provided he or she values the future sufficiently more than the opponent. This contrasts with the view that repetition induces cooperation, but conforms with the expectation that a more patient player receives a larger share of the pie. (shrink)

This paper deals with the equilibria of games when the agents have multiple objectives and, therefore, their utilities cannot be represented by a single value, but by a vector containing the various dimensions of the utility. Our approach allows the incorporation of partial information about the preferences of the agents into the model, and permits the identification of the set of equilibria in accordance with this information. We also propose an additional conservative criterion which can be applied (...) in this framework in order to predict the results of interaction. The potential application of the theoretical results is shown with an analysis of a mixed oligopoly in which the agents value additional objectives other than their own benefit. These objectives are related to social welfare and to the profit of the industry. The flexibility of our approach provides a general theoretical framework for the analysis of a wide range of strategic economic models. (shrink)

This paper introduces a new equilibrium concept for normal form games called dependency equilibrium; it is defined, exemplified, and compared with Nash and correlated equilibria in Sections 2–4. Its philosophical motive is to rationalize cooperation in the one shot prisoners' dilemma. A brief discussion of its meaningfulness in Section 5 concludes the paper. †To contact the author, please write to: Department of Philosophy, University of Konstanz, 78457 Konstanz, Germany; e-mail: [email protected].

This paper investigates the existence of pure strategy Nash equilibria in discontinuous and nonquasiconcave games. We introduce a new notion of continuity, called weakly continuous security, which is weaker than the most known weak notions of continuity, including the surrogate point secure of SSYM game of Carbonell-Nicolau and Mclean (Econ Theory, 2018a), the continuous security of Barelli and Meneghel (Econometrica 81:813–824, 2013), C-security of McLennan et al. (Econometrica 79:1643–1664 2011), generalized weakly transfer continuity of Nessah (Economics 47:659–662, 2011), (...) generalized better-reply security of Carmona (Econ Theory 48:1–4, 2011), Barelli and Soza (On the existence of Nash equilibria in discontinuous and qualitative games, 2009), Barelli and Meneghel (Econometrica 81:813–824, 2013), lower single deviation property of Reny (Further results on the existence of Nash equilibria in discontinuous games. University of Chicago, 2009), better-reply security of Reny (Econometrica 67:1029–1056, 1999) and the results of Prokopovych (Econ Theory 48:5–16, 2011, Econ Theory 53:383–402, 2013) and Carmona (J Econ Theory 144:1333–1340, 2009). We show that a compact, convex and weakly continuous secure Hausdorff locally convex topological vector space game has a pure strategy Nash equilibrium. Moreover, it holds in a large class of discontinuous games. (shrink)

This paper takes a novel approach to studying the existence and stability of Nash equilibria in N-firm Cournot–Bertrand oligopolies. First, we show that such games can be monotonically embedded into a game of strategic heterogeneity, so that each firm best responds to the choices of all other firms in a monotonic way. We then show that this monotonicity can be exploited to derive conditions which guarantee the existence of a unique, dominance solvable Nash equilibrium which is stable (...) under all adaptive dynamics. These conditions constitute a strict improvement over existing results in the literature. Finally, we examine the effect on these conditions resulting from additional firms entering the market. (shrink)

A simple Weberian agglomeration is developed and then extended as an innovative fixed-charged, colocation model over a large set of locational possibilities. The model is applied to cases in which external economies (EE) arise due to colocation alone and also cases in which EE arise due to city size. Solutions to the model are interpreted in the context of contemporary equilibrium analysis, which allows Weberian agglomeration to be interpreted in a more general way than in previous analyses. Within that context, (...) the Nash points and Pareto efficient points in the location patterns derived in the model are shown to rarely coincide. The applications consider agglomeration from two perspectives: one is the colocation behavior of producers as the agents of agglomeration and the other is the interaction between government and those agents in the interest of agglomeration policy. Extending the analysis to games, potential Pareto efficiency and Hicks optimality are considered with respect to side payments between producers and with respect to appropriate government incentives toward agglomeration. (shrink)

The notion of Nash equilibrium in static oligopoly games is based on the assumption that each firm knows its entire demand curve (and, therefore, its entire profit function). It is much more likely, however, that firms only have some idea of the outcome of small price variations within some relatively small interval of prices. This is because firms can only learn their demand functions through price experiments and if they are risk-averse and/or have a low discount factor, they will (...) be unwilling to engage in extensive price experiments involving large variations in price. We can therefore expect firms to experiment through small price variations and stop when they reach a price such that no small deviation.. (shrink)

The failure of models based on rational expectations to explain the ‘boom and bust’ of financial markets does not support Soros' critique of mainstream economics or his call for a theoretical revolution. Contrary to what Soros says, standard rational choice theory has the conceptual resources to analyse reflexivity. The dynamic of feedback loops for example can be described by simple models based on multiple equilibria and informational cascades. The problem is that agents and theorists sometimes lack the information (...) required to identify equilibria and tipping points. (shrink)

Game-theoretic solution concepts such as Nash and Bayesian equilibrium start from an assumption that the players’ sets of possible payoffs, measured in units of von Neumann–Morgenstern utility, are common knowledge, and they go on to define rational behavior in terms of equilibrium strategy profiles that are either pure or independently randomized and which, in applications, are often taken to be uniquely determined or at least tightly constrained. A mechanism through which to obtain a common knowledge of payoff functions measured (...) in units of utility is not part of the model. This paper describes an operational method of constructing a state of common knowledge of the key parameters of the players’ utility functions in terms of conditional small bets on the game’s outcome. When the rationality criterion of joint coherence is applied in this setting, the solution of a game is typically characterized by a convex set of correlated equilibria. In the most general case, where players are risk averse, the parameters of the equilibria are risk-neutral probabilities, interpretable as products of subjective probabilities and relative marginal utilities for money, as in financial markets. Risk aversion generally enlarges the set of equilibria and may present opportunities for Pareto-improving modifications of the rules of the game. (shrink)

The potential of the soil to hold plant nutrients is governed by the cation-exchange capacity of any soil. Estimating soil CEC aids in conventional soil management practices to replenish the soil solution that supports plant growth. In this study, a multiple model integration scheme supervised with a hybrid genetic algorithm-neural network was developed and employed to predict the accuracy of soil CEC in Tabriz plain, an arid region of Iran. The standalone models and extreme learning machine ) were implemented (...) for incorporation into the MM-GANN. In addition, it was tested to enhance the prediction accuracy of the standalone models. The soil parameters such as clay, silt, pH, carbonate calcium equivalent, and soil organic matter were used as model inputs to predict soil CEC. With the use of several evaluation criteria, the results showed that the MM-GANN model involving the predictions of ELM and ANN models calibrated by considering all the soil parameters as inputs provided superior soil CEC estimates with a Nash Sutcliffe Efficiency = 0.87, Root Mean Square Error = 2.885, Mean Absolute Error = 2.249, Mean Absolute Percentage Error = 12.072, and coefficient of determination = 0.884. The proposed MM-GANN model is a reliable intelligence-based approach for the assessment of soil quality parameters intended for sustainability and management prospects. (shrink)

The theory of Punctuated Equilibria challenges the neo‐Darwinian tenet that evolution is a uniform process. Recently, an article by Hunt1 has found that directional change during the evolution of a lineage is relatively small (occurring only in 5% of 250 analyzed traits). Of those traits that were shown to follow a trend, size was more likely to show gradual changes, whereas shape changes were more random. Here, we provide a short view of the nature of evolutionary trends, showing that (...) directional change within lineages and among clades provides valuable evolutionary information about the processes involved in their generation. BioEssays 30:521–525, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

A pure-strategy equilibrium existence theorem is extended to include games with non-expected utility players. It is shown that to guarantee the existence of a Nash equilibrium in pure strategies, the linearity of preferences in the probabilities can be replaced by the weaker requirement of quasiconvexity in the probabilities.

This study aims to provide a manageable symmetric two-players conflict model in which, defining measures for polarization and hostility, we investigate the effects of spillovers into the properties of the sets of equilibria, into the intensity of conflict, and into the endogenous changes in polarization and hostility. We show that, without spillovers, the equilibrium efforts’ intensity is uniquely connected to the ratio of the marginal productivity of effort to (ex ante) polarization. Conversely, we show that negative spillovers in conflict (...) technology can imply the non-existence of equilibria. Then, introducing spillovers in the possible outcomes of the conflict, we connect the existence of multiple symmetric and asymmetric equilibria to the intensity of growing polarization and hostility. We then investigate the different effects of marginal productivity of effort, (ex ante) polarization and rates of growth of polarization and hostility on the intensity of conflict as well as on polarization and hostility at equilibrium. The results show the crucial role played by hostility, a factor disregarded in many conflict models. Finally, we show how the results obtained by considering partial spillover effects are confirmed when the general case is taken into account. (shrink)

We use game theory and Santa Fe Artificial Stock Market, an agent-based model of an evolving stock market, to study the optimal frequency for traders to revise their market forecasting rules. We discover two things: There is a unique strategic Nash equilibrium in the game of choosing forecast revision rates, and this equilibrium is sub-optimal in the sense that traders’ earnings are not maximized an the market is inefficient. This strategic equilibrium is due to an analogue of the prisoner’s (...) dilemma; the optimal global state is unstable because each trader has too much incentive to ‘defect’ and use forecasting rules that pull the market into thesub-optimal equilibrium. (shrink)

Nash equilibria with identical supports are compared for bimatrix games that are different with respect to the risk aversion of player 2. For equilibria in 2× 2-bimatrix games and for equilibria with efficient supports in coordination games it is established for which cases increased risk aversion of player 2 benefits or hurts player 2.

This article shows that social norms are better explained as correlating devices for a correlated equilibrium of the underlying stage game, rather than Nash equilibria. Whereas the epistemological requirements for rational agents playing Nash equilibria are very stringent and usually implausible, the requirements for a correlated equilibrium amount to the existence of common priors, which we interpret as induced by the cultural system of the society in question. When the correlating device has perfect information, we need (...) in addition only to posit that individuals obey the social norm when it is costless to do so. When the correlating device has incomplete information, the operation of the social norm requires that individuals have a predisposition to follow the norm even when this is costly. The latter case explains why social norms are associated with other-regarding preferences and provides a basis for analyzing honesty and corruption. (shrink)

This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies ( (...) class='Hi'>Nash, Proceedings of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players. (shrink)

Since the seminal paper of Nash (Proc Natl Acad Sci USA 36:48–49, 1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. In a recent paper of Pruzhansky (Int J Game Theory 40:351–365, 2011) it was shown that under fairy general conditions maximin strategies in completely mixed games can guarantee the same expected payoff as completely mixed Nash equilibrium strategies. Based on this finding, the current paper argues that maximin strategies have important properties. (...) For instance, maximin strategies may refine Nash equilibria in subjective mixed strategies. Further, Bayesian rationality of the players may favor maximin strategies more often than Nash equilibrium strategies. The paper concludes with several suggestions for further experimental research that may shed more light on whether maximin behavior can explain reality better than Nash equilibrium. (shrink)

How can players reach a Nash equilibrium? I offer one possible explanation in terms of a low-rationality learning method called probe and adjust by proving that it converges to strict Nash equilibria in an important class of games. This demonstrates that decidedly limited learning methods can support Nash equilibrium play.

We introduce the notion of an outcome space, in which strategic interactions are embedded. This allows us to investigate the idea that one strategic interaction might be an expanded version of another interaction. We then characterize the Nash equilibria arising in such extensions and demonstrate a folk-type theorem stating that any individually rational element of the outcome space is a Nash equilibrium.

Brian Skyrms constructs a theory of "dynamic deliberation" and uses it to investigate rational decision-making in cases of strategic interaction. This illuminating book will be of great interest to all those in many disciplines who use decision theory and game theory to study human behavior and thought. Skyrms begins by discussing the Bayesian theory of individual rational decision and the classical theory of games, which at first glance seem antithetical in the criteria used for determining action. In his effort to (...) show how methods for dealing with information feedback can be productively combined, the author skillfully leads us through the mazes of equilibrium selection, the Nash equilibria for normal and extensive forms, structural stability, causal decision theory, dynamic probability, the revision of beliefs, and, finally, good habits for decision. The author provides many clarifying illustrations and a handy appendix called "Deliberational Dynamics on Your Personal Computer." His powerful model has important implications for understanding the rational origins of convention and the social contract, the logic of nuclear deterrence, the theory of good habits, and the varied strategies of political and economic behavior. (shrink)

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of "quantifying into" (...) epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies. (shrink)

In the literature of collective intentions, the ‘we-intentions’ that lie behind cooperative actions are analysed in terms of individual mental states. The core forms of these analyses imply that all Nash equilibrium behaviour is the result of collective intentions, even though not all Nash equilibria are cooperative actions. Unsatisfactorily, the latter cases have to be excluded either by stipulation or by the addition of further, problematic conditions. We contend that the cooperative aspect of collective intentions is not (...) a property of the intentions themselves, but of the mode of reasoning by which they are formed. We analyse collective intentions as the outcome of team reasoning, a mode of practical reasoning used by individuals as members of groups. We describe this mode of reasoning in terms of formal schemata, discuss a range of possible accounts of group agency, and show how existing theories of collective intentions fit into this framework. (shrink)

In its classical conception, game theory aspires to be a determinate decision theory for games, understood as elements of a structurally specified domain. Its aim is to determine for each game in the domain a complete solution to each player's decision problem, a solution valid for all real-world instantiations, regardless of context. "Permissiveness" would constrain the theory to designate as admissible for a player any conjecture consistent with the function's designation of admissible strategies for the other players. Given permissiveness and (...) other appropriate constraints, solution sets must contain only Nash equilibria and at least one pure-strategy equilibrium, and there is no solution to games in which no symmetry invariant set of pure-strategy equilibria forms a Cartesian product. These results imply that the classical program is unrealizable. Moreover, the program is implicitly committed to permissiveness, through its common-knowledge assumptions and its commitment to equilibrium. The resulting incoherence deeply undermines the classical conception in a way that consolidates a long series of contextualist criticisms. (shrink)

We study a low-rationality learning dynamics called probe and adjust. Our emphasis is on its properties in games of information transfer such as the Lewis signaling game or the Bala-Goyal network game. These games fall into the class of weakly better reply games, in which, starting from any action profile, there is a weakly better reply path to a strict Nash equilibrium. We prove that probe and adjust will be close to strict Nash equilibria in this class (...) of games with arbitrarily high probability. In addition, we compare these asymptotic properties to short-run behavior. (shrink)

Issues that arise in using game theory to model national security problems are discussed, including positing nation-states as players, assuming that their decision makers act rationally and possess complete information, and modeling certain conflicts as two-person games. A generic two-person game called the Conflict Game, which captures strategic features of such variable-sum games as Chicken and Prisoners'' Dilemma, is then analyzed. Unlike these classical games, however, the Conflict Game is a two-stage game in which each player can threaten to retaliate (...) — and carry out this threat in the second stage — if its opponent chose noncooperation in the first stage.Conditions for the existence of different pure-strategy Nash equilibria, or stable outcomes, are found, and these results are extended to situations in which the players can select mixed strategies (i.e., make probabilistic threats or choices). Although the Conflict Game sheds light on the rational foundations underlying arms races, nuclear deterrence, and other strategic situations, more detailed assumptions are required to tie this generic game to specific conflicts. (shrink)