Implementation, elimination of weakly dominated strategies and evolutionary dynamics

This paper is concerned with the realism of mechanisms that implement social choice functions in the traditional sense. Will agents actually play the equilibrium assumed by the analysis? As an example, we study the convergence and stability properties of Sj\"ostr\"om's (1994) mechanism, on the assumption that boundedly rational players find their way to equilibrium using monotonic learning dynamics and also with fictitious play. This mechanism implements most social choice functions in economic environments using as a solution concept the iterated elimination of weakly dominated strategies (only one round of deletion of weakly dominated strategies is needed). There are, however, many sets of Nash equilibria whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics we show that many equilibria in all the sets of equilibria we describe are the limit points of trajectories that have completely mixed initial conditions. The initial conditions that lead to these equilibria need not be very close to the limiting point. Furthermore, even if the dynamics converge to the ``right'' set of equilibria, it still can converge to quite a poor outcome in welfare terms. With fictitious play, if the agents have completely mixed prior beliefs, beliefs and play converge to the outcome the planner wants to implement.Implementation, bounded rationality, evolutionary dynamics, mechanisms

IMPLEMENTATION, ELIMINATION OF WEAKLY DOMINATED STRATEGIES AND EVOLUTIONARY DYNAMICS

This paper studies convergence and stability properties of Sjöström's (1994) mechanism, under the assumption that boundedly rational players find their way to equilibrium using monotonic learning dynamics and best-reply dynamics. This mechanism implements most social choice functions in economic environments using as a solution concept one round of deletion of weakly dominated strategies and one round of deletion of strictly dominated strategies. However, there are other sets of Nash equilibria, whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics, all these sets of equilibria contain limit points of the learning dynamics. Furthermore, even if the dynamics converge to the "right" set of equilibria (i.e. the one which contains the solution of the mechanism), it may converge to an equilibrium which is worse in welfare terms. In contrast with this result, any interior solution of the best-reply dynamics converges to the equilibrium whose outcome the planner desires.Implementation Theory, Evolutionary Dynamics

Splitting The Baby In Two: How To Solve Solomon'S Dilemma When Agents Are Boundedly Rational

We study the dynamic implementation of the first-best for King Solomon's Dilemma, on the assumption that boundedly rational players find their way to equilibrium using monotonic evolutionary dynamics, and also with best-reply dynamics. We find that, although the mechanisms proposed by the literature are dynamically implementable with best-reply dynamics, the same does not hold when monotonic dynamics are considered. To solve this problem, we propose an alternative mechanism, whose game-form is still implementable in the traditional sense. However, it is also dynamically implementable, as every interior path of the adjustment pro-cesses we consider converges to the first-best, which is also asymptotically stable.We study the dynamic implementation of the first-best for King Solomon's Dilemma, on the assumption that boundedly rational players find their way to equilibrium using monotonic evolutionary dynamics, and also with best-reply dynamics. We find that, although the mechanisms proposed by the literature are dynamically implementable with best-reply dynamics, the same does not hold when monotonic dynamics are considered. To solve this problem, we propose an alternative mechanism, whose game-form is still implementable in the traditional sense. However, it is also dynamically implementable, as every interior path of the adjustment pro-cesses we consider converges to the first-best, which is also asymptotically stable.Refereed Working Papers / of international relevanc

SOLOMON'S DILEMMA: AN EXPERIMENTAL STUDY ON DYNAMIC IMPLEMENTATION

This paper reports an experimental investigation on two mechanisms for the so-called King Solomon Dilemma, where one of them fails to implement the social choice rule dynamically. We compare the two mechanisms in terms of their welfare, incentive and learning properties.experiments, implementation, backward induction, bounded rationality

- CONTINUOUS-TIME EVOLUTIONARY DYNAMICS: THEORY AND PRACTICE

This paper surveys some recent developments in the literature which studies continuous-timeevolutionary dynamics in the context of economic modeling.Evolutionary Game Theory, Equilibrium Analysis, Bounded Rationality

Social Preferences and Strategic Uncertainty: An Experiment on Markets and Contracts

This paper reports experimental evidence on a stylized labor market. The experiment is designed as a sequence of three phases. In the rst two phases, P1 and P2; agents face simple games, which we use to estimate subjects social and reciprocity concerns, together with their beliefs. In the last phase, P3; four principals, who face four teams of two agents, compete by o¤ering agents a contract from a xed menu. Then, each agent selects one of the available contracts (i.e. he "chooses to work" for a principal). Production is determined by the outcome of a simple effort game induced by the chosen contract. We nd that (heterogeneous) social preferences are signi cant determinants of choices in all phases of the experiment. Since the available contracts display a trade-of between fairness and strategic uncertainty, we observe that the latter is a much stronger determinant of choices, for both principals and agents. Finally, we also see that social preferences explain, to a large extent, matching between principals and agents, since agents display a marked propensity to work for principals with similar social preferences

Social Preferences and Strategic Uncertainty: An Experiment on Markets and Contracts

This paper reports experimental evidence on a stylized labor market. The experiment is designed as a sequence of three phases. In the rst two phases, P1 and P2; agents face simple games, which we use to estimate subjects social and reciprocity concerns, together with their beliefs. In the last phase, P3; four principals, who face four teams of two agents, compete by o¤ering agents a contract from a xed menu. Then, each agent selects one of the available contracts (i.e. he "chooses to work" for a principal). Production is determined by the outcome of a simple effort game induced by the chosen contract. We nd that (heterogeneous) social preferences are signi cant determinants of choices in all phases of the experiment. Since the available contracts display a trade-of between fairness and strategic uncertainty, we observe that the latter is a much stronger determinant of choices, for both principals and agents. Finally, we also see that social preferences explain, to a large extent, matching between principals and agents, since agents display a marked propensity to work for principals with similar social preferences

Strategic Interaction and Conventions

The scope of the paper is to review the literature that employs coordination games to study social norms and conventions from the viewpoint of game theory and cognitive psychology. We claim that those two alternative approaches are complementary, as they provide different insights to explain how people converge to a unique system of self-fulfilling expectations in presence of multiple, equally viable, conventions. While game theory explains the emergence of conventions relying on efficiency and risk considerations, the psychological view is more concerned with frame and labeling effects. The interaction between these alternative (and, sometimes, competing) effects leads to the result that coordination failures may well occur and, even when coordination takes place, there is no guarantee that the convention eventually established will be the most efficient.Behavioral Game Theory, conventions, social norms

An experiment on markets and contracts : do social preferences determine corporate culture?

This paper reports experimental evidence on a stylized labor market. The experiment is designed as a sequence of three treatments. In the last treatment, TR3, four principals, who face four teams of two agents, compete by offering the agents a contract from a fixed menu. In this menu, each contract is the optimal solution of a (complete information) mechanism design problem where principals face agents’ who have social (i.e. interdependent) distributional preferences a’ la Fehr and Schmidt [19] with a specific parametrization. Each agent selects one of the available contracts offered by the principals (i.e. he “chooses to work” for a principal). Production is determined by the outcome of a simple effort game induced by the chosen contract. In the first two treatments, TR1 and TR2, we estimate individual social preference parameters and beliefs in the effort game, respectively. We find that social preferences are significant determinants of the matching process between labor supply and demand in the market stage, as well as principals’ and agents’ contract and effort decisions. In addition, we also see that social preferences explain the matching process in the labor market, as agents display a higher propensity to choose to work for a principal with similar distributional preferences.

Social vs. Risk Preferences under the Veil of Ignorance

This paper reports experimental evidence from a series of a simple Dictator Games in which, randomly matched in pair, subjects choose repeatedly one out of four alternatives involving a pair of fixed monetary prizes, one for them and the other for an anonymously matched subject. While in some treatments player position (i.e. the identity of the best paid agent) is known in advance before subjects have to select their favorite option, in one treatment subjects choose under “the veil of ignorance”, only knowing that either role is equally likely. Finally, we also collect evidence from another treatment, in which the same options correponds to binary lotteries, in which subjects may win one prize or the other with equal probability.This paper reports experimental evidence from a series of a simple Dictator Games in which, randomly matched in pair, subjects choose repeatedly one out of four alternatives involving a pair of fixed monetary prizes, one for them and the other for an anonymously matched subject. While in some treatments player position (i.e. the identity of the best paid agent) is known in advance before subjects have to select their favorite option, in one treatment subjects choose under “the veil of ignorance”, only knowing that either role is equally likely. Finally, we also collect evidence from another treatment, in which the same options correponds to binary lotteries, in which subjects may win one prize or the other with equal probability.Non-Refereed Working Papers / of national relevance onl