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The theory of full implementation has been criticized for using integer/modulo games which admit no equilibrium (Jackson (1992)). To address the critique, we revisit the classical Nash implementation problem due to Maskin (1977, 1999) but allow for the use of lotteries and monetary transfers as in Abreu and Matsushima (1992, 1994). We unify the two well-established but somewhat orthogonal approaches in full implementation theory. We show that Maskin monotonicity is a necessary and sufficient condition for (exact) mixed-strategy Nash implementation by a finite mechanism. In contrast to previous papers, our approach possesses the following features: finite mechanisms (with no integer or modulo game) are used; mixed strategies are handled explicitly; neither undesirable outcomes nor transfers occur in equilibrium; the size of transfers can be made arbitrarily small; and our mechanism is robust to information perturbations.

We discuss the identification and estimation of discrete games of complete information. Following Bresnahan and Reiss (1990,1991), a discrete game is a generalization of a standard discrete choice model where utility depends on the actions of other players. Using recent algorithms to compute all of the Nash equilibria to a game, we propose simulation-based estimators for static, discrete games. We demonstrate that the model is identified under weak functional form assumptions using exclusion restrictions and an identification at infinity approach. Monte Carlo evidence demonstrates that the estimator can perform well in moderately sized samples. As an application, we study entry decisions by construction contractors to bid on highway projects in California. We find that an equilibrium is more likely to be observed if it maximizes joint profits, has a higher Nash product, uses mixed strategies, and is not Pareto dominated by another equilibrium.

It is sometimes the case that one solution concept in game theory is equivalent to applying another solution concept to a modified version of the game. In such cases, does it make sense to study the former separately (as it applies to the original representation of the game), or should we entirely subordinate it to the latter? The answer probably depends on the particular circumstances, and indeed the literature takes different approaches in different cases. In this article, I consider the specific example of Stackelberg mixed strategies. I argue that, even though a Stackelberg mixed strategy can also be seen as a subgame perfect Nash equilibrium of a corresponding extensive-form game, there remains significant value in studying it separately. The analysis of this special case may have implications for other solution concepts.

We compare the voluntary contribution mechanism with any mechanism attaining Pareto-efficient allocations when each agent can choose whether he/she participates in the mechanism for the provision of a non-excludable public good. We find that, in our participation game, the voluntary contribution mechanism, because of its higher participation probability in the unique symmetric mixed strategy Nash equilibrium, may perform better than any Pareto-efficient mechanism in terms of the equilibrium expected provision level of the public good and the equilibrium expected payoff of each agent. Our results suggest that the voluntary contribution mechanism, which cannot realize Pareto-efficient allocations under compulsory participation, might be superior to any Pareto-efficient mechanism if we allow agents to voluntarily choose participation in the mechanism.

Game-theoretic models are a convenient tool to systematically analyze competitive situations. This makes them particularly handy in the field of security where a company or a critical infrastructure wants to defend against an attacker. When the optimal solution of the security game involves several pure strategies (i.e., the equilibrium is mixed), this may induce additional costs. Minimizing these costs can be done simultaneously with the original goal of minimizing the damage due to the attack. Existing models assume that the attacker instantly knows the action chosen by the defender (i.e., the pure strategy he is playing in the i-th round) but in real situations this may take some time. Such adversarial inertia can be exploited to gain security and save cost. To this end, we introduce the concept of information delay, which is defined as the time it takes an attacker to mount an attack. In this period it is assumed that the adversary has no information about the present state of the system, but only knows the last state before commencing the attack. Based on a Markov chain model we construct strategy policies that are cheaper in terms of maintenance (switching costs) when compared to classical approaches. The proposed approach yields slightly larger security risk but overall ensures a better performance. Furthermore, by reinvesting the saved costs in additional security measures it is possible to obtain even more security at the same overall cost.

This paper examines repeated implementation of a social choice function (SCF) with infinitely lived agents whose preferences are determined randomly in each period. An SCF is repeatedly implementable in Nash equilibrium if there exists a sequence of (possibly history-dependent) mechanisms such that its Nash equilibrium set is nonempty and every equilibrium outcome path results in the desired social choice at every possible history of past play and realizations of uncertainty. We show, with minor qualifications, that in the complete information environment an SCF is repeatedly implementable in Nash equilibrium if and only if it is efficient. We also discuss several extensions of our analysis.

The Colonel Blotto game captures strategic situations in which players attempt to mismatch an opponent's action. We extend Colonel Blotto to a class of General Blotto games that allow for more general payoffs and externalities between fronts. These extensions make Blotto applicable to a variety of real-world problems. We find that like Colonel Blotto, most General Blotto games do not have pure strategy equilibria. Using a replicator dynamics learning model, we show that General Blotto may have more predictable dynamics than the original Blotto game. Thus, adding realistic structure to Colonel Blotto may, paradoxically, make it less complex.

We consider a game in which each of n players is invited to a meeting, and has to decide whether or not to attend the meeting. A quorum has to be at-tained if the meeting is to have the power of making binding decisions. We consider all possible preferences of the players. These preferences are assumed to be the same for all players. Restricting ourselves to symmetric Nash equilibria, we identify three different classes of preferences. In a first class the game has a unique Nash equilibrium, defined in mixed strategies. In a second class the game has two Nash equilibria, defined in pure strategies. In a final class of preferences the game has a Nash equilibrium in pure strategies, and possibly also in mixed strategies. If there is a mixed strategy Nash equilibrium, we show that the equilibrium probability of attending the meeting increases when the quorum increases. Furthermore, if the number of players becomes very large, this equilibrium probability tends to the value of the quorum. Finally, we show how the underlying game structure can also be used in other applications.