Payoff Information and Learning in Signaling Games

We add the assumption that players know their opponents' payoff functions and rationality to a model of non-equilibrium learning in signaling games. Agents are born into player roles and play against random opponents every period. Inexperienced agents are uncertain about the prevailing distribution of opponents' play, but believe that opponents never choose conditionally dominated strategies. Agents engage in active learning and update beliefs based on personal observations. Payoff information can refine or expand learning predictions, since patient young senders' experimentation incentives depend on which receiver responses they deem plausible. We show that with payoff knowledge, the limiting set of long-run learning outcomes is bounded above by rationality-compatible equilibria (RCE), and bounded below by uniform RCE. RCE refine the Intuitive Criterion (Cho and Kreps, 1987) and include all divine equilibria (Banks and Sobel, 1987). Uniform RCE sometimes but not always exists, and implies universally divine equilibrium.Comment: This material was previously part of a larger paper titled "Type-Compatible Equilibria in Signalling Games," which split into two smaller papers: "Learning and Type Compatibility in Signaling Games" and "Payoff Information and Learning in Signaling Games.

Bounded Rationality in Concurrent Parity Games

We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider omega-regular winning conditions given as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory and infinite-precision. We study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(n^{2d+3}) time, where n is the size of the game and 2d is the number of priorities, and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP cap coNP. While this complexity is the same as for the simpler class of turn-based games, where in each state only one of the players has a choice of moves, our algorithms, that are obtained by characterization of the winning sets as mu-calculus formulas, are considerably more involved

Conformity and Bounded Rationality in Games with Many Players

Intepret a set of players all playing the same pure strategy and all with similar attributes as a society. Is it consistent with self interested behaviour for a population to organise itself into a relatively small number of societies? In a companion paper we characterized how large " must be, in terms of parameters describing individual games, for an equilibrium to exhibit conformity in pure strategies. In this paper we provide a wide class of games where such conformity is boundedly rational, that is, where " can be chosen to be small.

Strategic equivalence and bounded rationality in extensive form games

In a large family of solution concepts for boundedly rational players --- allowing players to be imperfect optimizers, but requiring that ``better'' responses are chosen with probabilities at least as high as those of ``worse'' responses --- most of Thompson's ``inessential'' transformations for the strategic equivalence of extensive form games become far from inconsequential. Only two of the usual elementary transformations remain truly inessential: the interchange of moves, and replacing a final move by nature by simply taking expected payoffs.Extensive form games; Quantal response equilibrium; Logit model; Strategic equivalence

The neural basis of bounded rational behavior

Bounded rational behaviour is commonly observed in experimental games and in real life situations. Neuroeconomics can help to understand the mental processing underlying bounded rationality and out-of-equilibrium behaviour. Here we report results from recent studies on the neural basis of limited steps of reasoning in a competitive setting – the beauty contest game. We use functional magnetic resonance imaging (fMRI) to study the neural correlates of human mental processes in strategic games. We apply a cognitive hierarchy model to classify subject’s choices in the experimental game according to the degree of strategic reasoning so that we can identify the neural substrates of different levels of strategizing. We found a correlation between levels of strategic reasoning and activity in a neural network related to mentalizing, i.e. the ability to think about other’s thoughts and mental states. Moreover, brain data showed how complex cognitive processes subserve the higher level of reasoning about others. We describe how a cognitive hierarchy model fits both behavioural and brain data.Game theory, Bounded rationality, Neuroeconomics

An Explanation of Anomalous Behavior in Binary-Choice Games: Entry, Voting, Public Goods, and the Volunteers' Dilemma

This paper characterizes behavior with "noisy" decision making for a general class of N-person, binary-choice games. Applications include: participation games, voting, market entry, binary step-level public goods games, the volunteer's dilemma, the El Farol problem, etc. A simple graphical device is used to derive comparative statics and other theoretical properties of a "quantal response" equilibrium, and the resulting predictions are compared with Nash equilibria that arise in the limiting case of no noise. Many anomalous data patterns in laboratory experiments based on these games can be explained in this manner.participation games, entry, voting, step-level public goods games, volunteers' dilemma, quantal response equilibrium, El Farol problem, bounded rationality.

Convex Approximation of Bounded Rational Equilibria

In this paper, we consider the existence of a sequence of convex sets that has an approximation property for the equilibrium sets in the bounded rational environments. We show that the bounded rational equilibrium multivalued map is approximated with arbitrary precision in the abstract framework, a parameterized class of "general games" together with an associated abstract rationality function that is established by Anderlini and Canning (2001). As an application, we show that the existence of a selection for some bounded rational equilibria on a discontinuous region P when P is a perfect set.Convex Approximation, Bounded Rational Equilibria, Selection

Less Rationality, More Efficiency: a Laboratory Experiment on "Lemon" Markets.

We have experimentally tested a theory of bounded rational behavior in a "lemon market". It provides an explanation for the observation that real world players successfully conclude transactions when perfect rationality predicts a market collapse. We analyzed two different market designs : complete and partial market collapse. Our empirical observations deviate substantially from these theoretical predictions. In both markets, the participants traded more than theoretically predicted. Thus, the actual outcome is closer to efficiency than the theoretical prediction. Even after 20 repetitions of the first market constellation, the number of transactions did not drop to zero. Our bounded rationality approach to explain these observations starts with the insight that perfect rationality would require the players to perform an infinite number of iterative reasoning steps. Bounded rational players, however, carry out only a limited number of such iterations. We have determined the iteration type of the players independently from their market behavior. A significant correlation exists between iteration types and observed price offers. --guessing games,beauty contests,market failure,adverse selection,lemon problem,regulatory failure,paternalistic regulation

Voluntary Contributions by Consent or Dissent

We study games where voluntary contributions can be adjusted until a steady state is found. In consent games contributions start at zero and can be increased by consent, and in dissent games contributions start high and can be decreased by dissent. Equilibrium analysis predicts free riding in consent games but, in contrast, as much as socially efficient outcomes in dissent games. In our experiment, inexperienced subjects contribute high in consent games and low in dissent games, but behavior converges toward equilibrium predictions over time and eventually experienced subjects contribute as predicted: low in consent games and high in dissent games. Observed deviations from equilibrium in consent games are best explained by level-k reasoning, and those in dissent games are best explained by hierarchical reasoning formalized as nested logit equilibrium.public good, contribution game, bounded rationality, mechanism

Ten Little Treasures of Game Theory and Ten Intuitive Contradictions

This paper reports laboratory data for a series of two-person games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment for which behavior conforms quite nicely to the predictions of the Nash equilibrium or relevant refinement. In each case we change a key payoff parameter in a manner that does not alter the equilibrium predictions, but this theoretically neutral payoff change has a major (often dramatic) effect on observed behavior. These contradictions are generally consistent with simple economic intuition and with a model of iterated noisy introspection for one-shot games.Nash equilibrium, noncooperative games, experiments, bounded rationality, introspection