Efficiency in coalition games with externalities

A natural extension of superadditivity is not sufficient to imply that the grand coalition is efficient when externalities are present. We provide a condition, analogous to convexity, that is sufficient for the grand coalition to be efficient and show that this also implies that the (appropriately defined) core is nonempty. Moreover, we propose a mechanism which implements the most efficient partition for all coalition formation games and characterizes the resulting payoff division.     

Competition and coordination in experimental minority games

This work presents experimental results on a coordination game in which agents must repeatedly choose between two sides, and a positive fixed payoff is assigned only to agents who pick the minoritarian side. We conduct laboratory experiments in which stationary groups of five players play the game for 100 periods, and manipulate two treatment variables: the amount of information about other players’ past choices and the salience of information regarding the game history (i.e., the length of the string of past outcomes that players can see on the screen while choosing). Our main findings can be summarized as follows: aggregate efficiency in the game is in most cases significantly higher than the level corresponding to the symmetric mixed strategy Nash equilibrium. In addition, providing players with information about individual choices in the group does not improve aggregate efficiency with respect to when such information is absent. Displaying information about more rounds than just the previous one, on the other hand, seems to have a positive effect on aggregate efficiency. At the individual level, we find a stronger statistical relation between players’ current choices and their own past choices than between players’ choices and previous aggregate outcomes. In addition, the depth of the relation between present and past choices seems to be affected by the prompt availability of information about the game history. Finally, we detect evidence of a mutual co-adaptation between players’ choices over time that is partly responsible for the high level of efficiency observed.      

Melioration learning in games with constant and frequency-dependent pay-offs

The paper explores the implications of melioration learning—an empirically significant variant of reinforcement learning—for game theory. We show that in games with invariable pay-offs melioration learning converges to Nash equilibria in a way similar to the replicator dynamics. Since melioration learning is known to deviate from optimizing behavior when an action’s rewards decrease with increasing relative frequency of that action, we also investigate an example of a game with frequency-dependent pay-offs. Interactive melioration learning is then still appropriately described by the replicator dynamics, but it indeed deviates from rational choice behavior in such a game.     

Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

The value of commitment in Stackelberg games with observation costs

We study Stackelberg games in which the follower faces a cost for observing the leader's action. We show that, irrespective of the size of the cost, the leader's value of commitment is lost completely in all pure-strategy equilibria. However, there also exists a mixed-strategy equilibrium that fully preserves the first-mover advantage. In this type of equilibrium, the probability that the follower looks at the leader's action is independent of the cost of looking.