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

Rational reasoning or adaptive behavior? Evidence from two-person beauty contest games

Many experiments have shown that human subjects do not necessarily behave in line with game theoretic assumptions and solution concepts. The reasons for this non-conformity are multiple. In this paper we study the argument whether a deviation from game theory is because subjects are rational, but doubt that others are rational as well, compared to the argument that subjects, in general, are boundedly rational themselves. To distinguish these two hypotheses, we study behavior in repeated 2-person and many-person Beauty- Contest-Games which are strategically different from one another. We analyze four different treatments and observe that convergence toward equilibrium is driven by learning through the information about the other player’s choice and adaptation rather than self-initiated rational reasoning.Beauty contest, Guessing game, Bounded rationality, Weak dominance, Learning

English Auctions with toeholds: An experimental study

We run experiments on English Auctions where the bidders already own a part (toehold) of the good for sale. The theory predicts a very strong effect of even small toeholds, however we find the effects are not so strong in the lab. We explain this by analyzing the flatness of the payoff functions, which leads to relatively costless deviations from the equilibrium strategies. We find that a levels of reasoning model explains the results better than the Nash equilibrium. Moreover, we find that although big toeholds can be effective, the cost to acquire them might be higher than the strategic benefit they bring. Finally our results show that in general the seller’s revenues fall when the playing field is uneven.Experiments, toehold auction, takeover, payoff, flatness, quantal response, level-k, LeeX

An Experiment on Forward versus Backward Induction: How Fairness and Levels of Reasoning Matter

We report the experimental results on a game with an outside option where induction contradicts with background induction based on a focal, risk dominant equilibrium. The latter procedure yields the equilibrium selected by Harsanyi and Selton's (1888) theory, which is hence here in contradiction with strategic stability (Kohlberg-Mertens (1985)). We find the Harsanyi-Selton solution to be in much better agreement with our data. Since fairness and bounded rationality seem to matter we discuss whether recent behavioral theories, in particular fairness theories and learning, might explain our findings. The fairness theories by Fehr and Schmidt (1999), Bolton and Ockenfels (2000), when calibrated using experimental data on dictator- and ultimatum games, indeed predict that forward induction should play no role for our experiment and that the outside option should be chosen by all sufficiently selfish players. However, there is a multiplicity of "fairness equilibra", some of which seem to be rejected because they require too many levels of reasoning"experiments, equilibrium selection, forward induction, fairness, levels of reasoning.

No imitation - on local and group interaction, learning and reciprocity in prisoners\

This study disentangles experimentally imitation, reinforcement, and reciprocity in repeated prisoners' dilemmas. We compare a simple situation in which players interact only with their neighbours (local interaction) with one where players interact with all members of the population (group interaction). We observe choices under different information conditions and estimate parameters of a learning model. We find that imitation, while assumed to be a driving force in many models of spatial evolution, is often a negligible factor in the experiment. Behaviour is predominantly driven by reinforcement learning.Local interaction,experiments,prisoner's dilemma,learning,reinforcement,repeated games

An experimental study of adaptive behavior in an oligopolistic market game

We consider an oligopolistic market game, in which the players are competing firm in the same market of a homogeneous consumption good. The consumer side is represented by a fixed demand function. The firms decide how much to produce of a perishable consumption good, and they decide upon a number of information signals to be sent into the population in order to attract customers. Due to the minimal information provided, the players do not have a well--specified model of their environment. Our main objective is to characterize the adaptive behavior of the players in such a situation.Market game, oligopoly, adaptive behavior, learning, Leex

Equilibrium Selection Through Incomplete Information in Coordination Games: An Experimental Study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions.We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.Publicad

The effect of intergroup competition on group coordination: An experimental study

We report an experiment on the effect of intergroup competition on group coordination in the minimal-effort game (Van Huyck et al., 1990). The competition was between two 7-person groups. Each player in each group independently chose an integer from 1 to 7. The group with the higher minimum won the competition and each of its members was paid according to the game’s original payoff matrix. Members of the losing group were paid nothing. In case of a tie, each player was paid half the payoff in the original matrix. This treatment was contrasted with two control treatments where each of the two groups played an independent coordination game, either with or without information about the minimum chosen by the outgroup. Although the intergroup competition does not change the set of strict equilibria, we found that it improved collective rationality by moving group members in the direction of higher-payoff equilibria. Merely providing group members with information about the minimal-effort level in the other group was not sufficient to generate this effect.Non cooperative games, coordination, minimum effort game, intergroup competition, Leex

A Historical Note on the Beauty Contest

Alain Ledoux, who was one of over 6,000 chess players taking part in Bühren and Frank´s (2012) online Beauty Contest experiment, turned out to be the forgotten inventor of that game. We reconstruct the birth of the Beauty Contest. In section 1 of our note, its first two authors outline the history of the game that metamorphosed into the famous guessing game experiment which was first run in the lab by Rosemarie Nagel. In section 2, Rosemarie Nagel adds further remarks and thoughts about the development of the experimental Beauty Contest.