Rosemarie Nagel

Neural correlates of depth of strategic reasoning in medial prefrontal cortex

We used functional MRI (fMRI) to investigate human mental processes in a competitive interactive setting—the “beauty contest” game. This game is well-suited for investigating whether and how a players mental processing incorporates the thinking process of others in strategic reasoning. We apply a cognitive hierarchy model to classify subjects 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. According to this model, high-level reasoners expect the others to behave strategically, whereas low-level reasoners choose based on the expectation that others will choose randomly. The data show that high-level reasoning and a measure of strategic IQ (related to winning in the game) correlate with the neural activity in the medial prefrontal cortex, demonstrating its crucial role in successful mentalizing. This supports a cognitive hierarchy model of human brain and behavior.

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.

Measuring Strategic Uncertainty in Coordination Games

This paper explores three aspects of strategic uncertainty: its relation to risk, predictability of behavior and subjective beliefs of players. In a laboratory experiment we measure subjects’ certainty equivalents for three coordination games and one lottery. Behavior in coordination games is related to risk aversion, experience seeking, and age. From the distribution of certainty equivalents we estimate probabilities for successful coordination in a wide range of games. For many games, success of coordination is predictable with a reasonable error rate. The best response to observed behavior is close to the global-game solution. Comparing choices in coordination games with revealed risk aversion, we estimate subjective probabilities for successful coordination. In games with a low coordination requirement, most subjects underestimate the probability of success. In games with a high coordination requirement, most subjects overestimate this probability. Estimating probabilistic decision models, we show that the quality of predictions can be improved when individual characteristics are taken into account. Subjects’ behavior is consistent with probabilistic beliefs about the aggregate outcome, but inconsistent with probabilistic beliefs about individual behavior.

On the Robustness of Behaviour in Experimental ‘Beauty Contest’ Games

We report and compare results from several different versions of an experimental interactive guessing game first studied by Nagel (1995), which we refer to as the ‘beauty contest’ game following Keynes (1936). In these games, groups of subjects are repeatedly asked to simultaneously guess a real number in the interval [0, 100] that they believe will be closest to 1/2 times either the median, mean, or maximum of all numbers chosen. We also use our experimental data to test a simple model of adaptive learning behaviour.

The two-person beauty contest

We introduce a two-person beauty contest game with a unique Nash equilibrium that is identical to the game with many players. However, iterative reasoning is unnecessary in the two-person game as choosing zero is a weakly dominant strategy. Despite this “easier” solution concept, we find that a large majority of players do not choose zero. This is the case even with a sophisticated subject pool.

Choice of Partners in Multiple Two-Person Prisoner's Dilemma Games: An Experimental Study

We examine the effect of unilateral and mutual partner selection in the context of prisoners dilemmas experimentally. Subjects play simultaneously several finitely repeated two-person prisoners dilemma games. We find that unilateral choice is the best system. It leads to low defection and fewer singles than with mutual choice. Furthermore, with the unilateral choice setup we are able to show that intending defectors are more likely to try to avoid a match than intending cooperators. We compare our results of multiple games with single game PD-experiments and find no difference in aggregate behavior. Hence the multiple game technique is robust and might therefore be an important tool in the future for testing the use of mixed strategies.

Choice of Partners in Multiple Two-Person Prisoner's Dilemma Games

The effect of unilateral and mutual partner selection in the context of prisoners dilemmas is examined. Participants played simultaneously several finitely repeated, two-person prisoners dilemma games. Results show that unilateral choice leads to lower defection and fewer exits than mutual choice. In the unilateral-choice setup, intending defectors are more likely to exit than intending cooperators. Implications of these findings in the political context are discussed.

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.

Speculative Attacks and Financial Architecture:Experimental Analysis of Coordination Games with Public and Private Information

Speculative Attacks can be modeled as a coordination game with multiple equilibria if the state of the economy is common knowledge. With private information there is a unique equilibrium. This raises the question whether public information may be destabilizing by allowing for self-fulfilling beliefs. We present an experiment that imitates a speculative attacks model and compare sessions with public and private information. In both treatments subjects use so-called threshold strategies that lie in between the risk dominant and payoff dominant equilibrium of the underlying complete information game. Our evidence suggests that there are no destabilizing effects due to public information. In contrary, predictability of attacks is slightly higher with public than with private information, but prior probability of attacks is also higher with public information. We also test the predictive power of refinement theories to explain actual behavior and reactions to parameter changes.

Prosocial Capabilities in Alzheimer's Patients

OBJECTIVES To examine the decision making of Alzheimers patients in a simple, classic game focusing on their capabilities to implement social norms and common social preferences. METHODS Patients with Stage I (very mild and mild) Alzheimers disease (AD) were asked to participate in a dictator game, a type of game in which a subject has to decide how to allocate a certain amount of money between himself and another person. RESULTS When we compared the results of treatments involving AD patients (at an early stage) with those of identical treatments involving patients with mild cognitive impairment or healthy elderly controls, with similar ages and social backgrounds, we did not find statistically significant differences. DISCUSSION This finding suggests that Stage I AD patients are as capable of making decisions involving basic social norms and preferences as other individuals of their age. Whatever brain structures are affected by the disease, they do not appear to influence, at this early stage, the neural basis for cooperation-enhancing social interactions.