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.

Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

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 prisoner's dilemmas experimentally. Subjects play simultaneously several finitely repeated two-person prisoner's 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 intendingdefectors 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.

Market Index Biases and Minimum Risk Indices

Markets, in the real world, are not efficient zero-sum games where hypotheses of the CAPM are fulfilled. Then, it is easy to conclude the market portfolio is not located on Markowitz"s efficient frontier, and passive investments (and indexing) are not optimal but biased. In this paper, we define and analyze biases suffered by passive investors: the sample, construction, efficiency and active biases and tracking error are presented. We propose Minimum Risk Indices (MRI) as an alternative to deal with to market index biases, and to provide investors with portfolios closer to the efficient frontier, that is, more optimal investment possibilities. MRI (using a Parametric Value-at-Risk Minimization approach) are calculated for three stock markets achieving interesting results. Our indices are less risky and more profitable than current Market Indices in the Argentinean and Spanish markets, facing that way the Efficient Market Hypothesis. Two innovations must be outlined: an error dimension has been included in the backtesting and the Sharpe"s Ratio has been used to select the"best" MRI

Market Index Biases and Minimum Risk Indices

Markets, in the real world, are not efficient zero-sum games where hypotheses of the CAPM are fulfilled. Then, it is easy to conclude the market portfolio is not located on Markowitz"s efficient frontier, and passive investments (and indexing) are not optimal but biased. In this paper, we define and analyze biases suffered by passive investors: the sample, construction, efficiency and active biases and tracking error are presented. We propose Minimum Risk Indices (MRI) as an alternative to deal with to market index biases, and to provide investors with portfolios closer to the efficient frontier, that is, more optimal investment possibilities. MRI (using a Parametric Value-at-Risk Minimization approach) are calculated for three stock markets achieving interesting results. Our indices are less risky and more profitable than current Market Indices in the Argentinean and Spanish markets, facing that way the Efficient Market Hypothesis. Two innovations must be outlined: an error dimension has been included in the backtesting and the Sharpe"s Ratio has been used to select the"best" MRI

Hot vs. cold: Sequential responses and preference stability in experimental games

In experiments with two-person sequential games we analyzewhether responses to favorable and unfavorable actions dependon the elicitation procedure. In our hot treatment thesecond player responds to the first player s observed actionwhile in our cold treatment we follow the strategy method and have the second player decide on a contingent action foreach and every possible first player move, without firstobserving this move. Our analysis centers on the degree towhich subjects deviate from the maximization of their pecuniaryrewards, as a response to others actions. Our results show nodifference in behavior between the two treatments. We also findevidence of the stability of subjects preferences with respectto their behavior over time and to the consistency of theirchoices as first and second mover.

Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

Social preferences: Some simple tests and a new model

Departures from pure self interest in economic experiments have recently inspired models of "social preferences". We conduct experiments on simple two-person and three-person games with binary choices that test these theories more directly than the array of games conventionally considered. Our experiments show strong support for the prevalence of "quasi-maximin" preferences: People sacrifice to increase the payoffs for all recipients, but especially for the lowest-payoff recipients. People are also motivated by reciprocity: While people are reluctant to sacrifice to reciprocate good or bad behavior beyond what they would sacrifice for neutral parties, they withdraw willingness to sacrifice to achieve a fair outcome when others are themselves unwilling to sacrifice. Some participants are averse to getting different payoffs than others, but based on our experiments and reinterpretation of previous experiments we argue that behavior that has been presented as "difference aversion" in recent papers is actually a combination of reciprocal and quasi-maximin motivations. We formulate a model in which each player is willing to sacrifice to allocate the quasi-maximin allocation only to those players also believed to be pursuing the quasi-maximin allocation, and may sacrifice to punish unfair players.

Causal assessment in finite extensive-form games

Two finite extensive-form games are empirically equivalent when theempirical distribution on action profiles generated by every behaviorstrategy in one can also be generated by an appropriately chosen behaviorstrategy in the other. This paper provides a characterization ofempirical equivalence. The central idea is to relate a game's informationstructure to the conditional independencies in the empirical distributionsit generates. We present a new analytical device, the influence opportunitydiagram of a game, describe how such a diagram is constructed for a givenextensive-form game, and demonstrate that it provides a complete summaryof the information needed to test empirical equivalence between two games.

Retribution in a cheap-talk experiment

We use a two-person 3-stage game to investigate whether people choose to punish or reward another player by sacrificing money to increase or decrease the other person’s payoff. One player sends a message indicating an intended play, which is either favorable or unfavorable to the other player in the game. After the message, the sender and the receiver play a simultaneous 2x2 game. A deceptive message may be made, in an effort to induce the receiver to make a play favorable to the sender. Our focus is on whether receivers’ rates of monetary sacrifice depend on the process and the perceived sender’s intention, as is suggested by the literature on deception and procedural satisfaction. Models such as Rabin (1993), Sen (1997), and Charness and Rabin (1999) also permit rates of sacrifice to be sensitive to the sender’s perceived intention, while outcome-based models such as Fehr and Schmidt (1999) and Bolton and Ockenfels (1997) predict otherwise. We find that deception substantially increases the punishment rate as a response to an action that is unfavorable to the receiver. We also find that a small but significant percentage of subjects choose to reward a favorable action choice made by the sender.

Does affirmative action reduce effort incentives? A contest game analysis

In this paper a contest game with heterogeneous players is analyzed in which heterogeneity could be the consequence of past discrimination. Based on the normative perception of the heterogeneity there are two policy options to tackle this heterogeneity: either it is ignored and the contestants are treated equally, or affirmative action is implemented which compensates discriminated players. The consequences of these two policy options are analyzed for a simple two-person contest game and it is shown that the frequently criticized trade-off between affirmative action and total effort does not exist: Instead, affirmative action fosters effort incentives. A generalization to the n-person case and to a case with a partially informed contest designer yields the same result if the participation level is similar under each policy.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.