How to talk to multiple audiences

Stochastic fictitious play (SFP) assumes that agents do not try to influence the future play of their current opponents, an assumption that is justified by appeal to a setting with a large population of players who are randomly matched to play the game. However, the dynamics of SFP have only been analyzed in models where all agents in a player role have the same beliefs. We analyze the dynamics of SFP in settings where there is a population of agents who observe only outcomes in their own matches and thus have heterogeneous beliefs. We provide conditions that ensure that the system converges to a state with homogeneous beliefs, and that its asymptotic behavior is the same as with a single representative agent in each player role.     

Team reasoning without a hive mind

The theory of team reasoning has been developed to resolve a long-lasting niggle in orthodox game theory. Despite its intuitive appeal, the theory has received little attention from mainstream game theorists and economists to date. We believe that this is so because of two theoretic issues, which the theory of team reasoning itself needs to resolve. One of these presents a worry that the theory achieves its explanatory and predictive success by abandoning ontological individualism — a fundamental precept in mainstream economics, including game theory. Here we argue that the theory of team reasoning is compatible with ontological individualism. We show that the core principles of the theory — those that give rise to the above worry — are in fact implicitly assumed in some branches of orthodox game theory itself. We also argue against the methodological approach that construes team reasoning as involving a transformation of the interacting players’ payoffs in modelled games.     

Rewards and the private provision of public goods on dynamic networks

We study an evolutionary model of a public good game with rewards played on a network. Giving rewards to contributors transforms the game but gives rise to a second-order dilemma. By allowing for coevolution of strategies and network structure, the evolutionary dynamics operate on both structure and strategy. Players learn with whom to interact and how to act and can overcome the second-order dilemma. More specifically, the network represents social distance which changes as players interact. Through the change in social distance, players learn with whom to interact, which we model using reinforcement dynamics. We find that, for certain parameter constellations, a social institution, prescribing prosocial behavior and thus solving the second-order dilemma, can emerge from a population of selfish players. Due to the dynamic structure of the network, the institution has an endogenous punishment mechanism ensuring that defectors will be excluded from the benefits of the institution and the public good will be supplied efficiently.     

Kernel-based type spaces

Type space is of fundamental importance in epistemic game theory. This paper shows how to build type space if players approach the game in a way advocated by Bernheim's justification procedure. If an agent fixes a strategy profile of her opponents and ponders which of their beliefs about her set of strategies make this profile optimal, such an analysis is represented by kernels and yields disintegrable beliefs. Our construction requires that underlying space is Polish.     

Walras and Darwin: an odd couple?

General equilibrium theory and the evolutionary branches of economics and game theory take rather opposite positions in the spectrum covered by the economic science. However, we reveal and explore analogies between Darwinian dynamics and Walrasian tatonnement processes for pure exchange economies, as well as further analogies implied by these.     

How historical analogies in newspapers of five countries make sense of major events: 9/11, Mumbai and Tahrir Square

We analyze how historical analogies are used in the media to make sense of novel events. While earlier work focused on single case studies, this is the first quantitative analysis comparing historical analogies invoked in three events in newspapers from five countries. With very high intercoder reliability we found 881 invocations of historical analogies. We found an interesting contrast between the roles of historical analogies in foreign policy decision making vs. newspaper articles. When the task is advocacy for policy choice, a compelling historical analogy will be one in which the causal mechanisms are as similar as possible to the current situation so that similar actions are likely to lead to similar results. Instead, newspapers spend more time at the early stages of sense-making and help the audience understand just a few features of the current situation. Newspapers thus offer a much broader range of historical analogies without much regard to maximizing similarity.     

Bounded Rationality in Economics: A Game Theorist's View

In this paper, we argue that it is essential to incorporate bounded rationality into game theory. Game theory has been applied to aspects of economics such as industrial organizati on on the basis of the naive interpret ation of game theory, which requires players to be ideally rational in an extremely unrealistic way. We stress the importance of establishing the perceptive interpretation of game theory by taking boundedly rational players' inductive reasoning processes into account. We explain my recent work, Matsushima (1997), which shows that the subjective games perceived by players in the long run are entirely different from the true objective game, and are trivial games in the sense that there exists a strictly dominant and subjectively Pareto-efficient strategy profile among the set of pure strategy profiles.
JEL Classification Numbers: C70, C90, D43, D80     

Monotone imitation dynamics in large populations

We analyze a class of imitation dynamics with mutations for games with any finite number of actions, and give conditions for the selection of a unique equilibrium as the mutation rate becomes small and the population becomes large. Our results cover the multiple-action extensions of the aspiration-and-imitation process of Binmore and Samuelson [Muddling through: noisy equilibrium selection, J. Econ. Theory 74 (1997) 235–265] and the related processes proposed by Benaı¨m and Weibull [Deterministic approximation of stochastic evolution in games, Econometrica 71 (2003) 873–903] and Traulsen et al. [Coevolutionary dynamics: from finite to infinite populations, Phys. Rev. Lett. 95 (2005) 238701], as well as the frequency-dependent Moran process studied by Fudenberg et al. [Evolutionary game dynamics in finite populations with strong selection and weak mutation, Theoretical Population Biol. 70 (2006) 352–363]. We illustrate our results by considering the effect of the number of periods of repetition on the selected equilibrium in repeated play of the prisoner's dilemma when players are restricted to a small set of simple strategies.     

Co-evolution of Preferences and Information in Simple Games of Trust

In standard rational choice modelling decisions are made according to given information and preferences. In the model presented here the `information technology' of individual decision-makers as well as their preferences evolve in a dynamic process. In this process decisions are made rationally by players who differ in their informational as well as in their preference type. Relative success of alternative decisions feeds back on the type composition of the population which in turn influences rational decision-making. An indirect evolutionary analysis of an elementary yet important basic game of trust shows that under certain parameter constellations the population dynamics of the evolutionary process specify a unique completely mixed rest point. However, as opposed to previous studies of preference formation in the game of trust there is no convergence to but only circumventing the rest point if the informational status of individuals evolves rather than being chosen strategically.     

Procedural Rationality and Institutions: The Production of Norms by Means of Norms

This paper deals with a cognitivist approach to the problem of how social and economic institutions are formed. The economic framework I use is Simon's model of procedural rationality, integrating a cognitivist approach into a game structure. In game theory norms are seen as conventions, but not all institutions can be explained by game theory models. In cognition-based approaches, the creation and maintenance of institutions is the outcome of a search for satisficing norms. According to Simon and Newell (1972), agents faced with problems to solve visualise a problem as an area of potential situations to examine in order to establish analogical problem structures. In my approach, a norm can be defined within a system of norms that form in a historical-evolutionary dimension, suggesting a path in norm-forming processes.     

Team reasoning theory: an experimental analysis of common reason to believe and social distance

The aim of this paper is to study the role of the “common reason to believe” (Sugden in Philos Explor 16:165–181, 2003) and the reduction of social distance within the theory of team reasoning. The analysis draws on data collected through a Traveler’s Dilemma experiment. To study the role of the common reason to believe, players’ beliefs in their counterparts’ choices are elicited, and the correlation between the endorsement of team reasoning and beliefs is considered. The relation between social distance and team reasoning is analyzed by introducing a meeting between the two players after the game. We show that the common reason to believe appropriately explains the internal logic of team reasoning and that a reduction of social distance does not produce any statistically significant effect on the probability that team reasoning will be used.     

Endogenous group formation in experimental contests

We experimentally study endogenous alliance formation and contest effort choices in a generic three-player contest. Differences in intrinsic or extrinsic incentives to expend effort cause self-selection. Weakly motivated players have an incentive to enter into an alliance and to free-ride on strongly motivated players; hence, strong players prefer to stand alone. Self-selection has direct consequences for effort in endogenously formed alliances. But we also find evidence of an effort stimulating effect if players endogenously form an alliance, which is in line with theories of in-group favoritism. The experimental evidence on self-selection is in conformity with a theory analysis of the game.     

Equilibrium play and best response to (stated) beliefs in normal form games

We report experimental results on a series of ten one-shot two-person 3×3 normal form games with unique equilibrium in pure strategies played by non-economists. In contrast to previous experiments in which game theory predictions fail dramatically, a majority of actions taken coincided with the equilibrium prediction (70.2%) and were best-responses to subjects' stated beliefs (67.2%). In constant-sum games, 78% of actions taken were predicted by the equilibrium model, outperforming simple K-level reasoning models. We discuss how non-trivial game characteristics related to risk aversion, efficiency concerns and social preferences may affect the predictive value of different models in simple normal form games.     

A spectrum of equilibration processes in game theory

In game theory, four dynamic processes converging towards an equilibrium are distinguished and ordered by way of agents' decreasing cognitive capacities. In the eductive process, each player has enough information to simulate perfectly the others' behavior and gets immediately to the equilibrium. In epistemic learning, each player updates his beliefs about others' future strategies, with regard to their sequentially observed actions. In behavioral learning, each player modifies his own strategies according to the observed payoffs obtained from his past actions. In the evolutionary process, each agent has a fixed strategy and reproduces in proportion to the utilities obtained through stochastic interactions. All along the spectrum, longer term dynamics makes up for weaker rationality, and physical relations substitute for mental interactions. Convergence, if any, is towards an always stronger equilibrium notion and selection of an equilibrium state becomes more sensitive to context and history. The processes can be mixed if associated to different periods, agents or mechanisms and deepened if obtained by formal reasoning principles.     

Dynamics of inductive inference in a unified framework

We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rule-based reasoning. This unified framework allows us to examine how the various modes of inductive inference can be combined and how their relative weights change endogenously. For example, we establish conditions under which an agent who does not know the structure of the data generating process will decrease, over the course of her reasoning, the weight of credence put on Bayesian vs. non-Bayesian reasoning. We illustrate circumstances under which probabilistic models are used until an unexpected outcome occurs, whereupon the agent resorts to more basic reasoning techniques, such as case-based and rule-based reasoning, until enough data are gathered to formulate a new probabilistic model.     

Corporate Control and the Decapitalization of Subsidiary Corporations: The Looting of the Bangor and Aroostook Railroad

John Rawls's A Theory of Justice is examined from the perspective of experimental methods in economics and complex adaptive systems simulations. This paper first discusses the justice principle selection process in Rawls's representation of it as a hypothetical experiment. This hypothetical experiment fails to satisfy reasonable experimental controls, particularly as reflects the conception of the individual it employs. The second section of the paper discusses the differences between Rawls's two conceptions of rational persons associated with his distinction between thin and full theories of the good. The third section uses his fuller conception of rational persons, life plans, and psychological laws in the third part of the book to offer an alternative view of the selection process understood as a complex adaptive system. The fourth section turns to a topic raised by this complex system approach, the status of normative reasoning in political-economic systems. The fifth section summarizes.     

Resolving Indeterminacy in Coordination Games: A New Approach Applied to a Pay-as-you-go Pension Scheme

This paper shows that when players ignore what outcome will emerge because of the presence of multiple equilibria, they can coordinate their expectations by forming an initial belief based on the principle of indifference followed by a process of reasoning that updates this belief. Since this procedure describes a natural way to form beliefs under indeterminacy, it is reasonable for every agent to conjecture that all the others form their beliefs according to the same logic. Exactly the fact that agents are aware that they form their beliefs following the same procedure allows them to successfully coordinate their expectations.      

Adaptation and complexity in repeated games

The paper presents a learning model for two-player infinitely repeated games. In an inference step players construct minimally complex inferences of strategies based on observed play, and in an adaptation step players choose minimally complex best responses to an inference. When players randomly select an inference from a probability distribution with full support the set of steady states is a subset of the set of Nash equilibria in which only stage game Nash equilibria are played. When players make ‘cautious’ inferences the set of steady states is the subset of self-confirming equilibria with Nash outcome paths. When players use different inference rules, the set of steady states can lie between the previous two cases.     

Learning from Personal Experience: One Rational Guy and the Justification of Myopia

The paper examines a large population analog of fictitious play in which players learn from personal experience, focusing on what happens when a single rational player is added to the population. Because the learning process naturally generates contagion dynamics, the rational player at times has an incentive to act nonmyopically. In 2 × 2 games the dynamics are asymmetric and favor risk dominant equilibria. A variety of other examples are presented.Journal of Economic LiteratureClassification Number: C7.