Implementability of Correlated and Communication Equilibrium Outcomes in Incomplete Information Games

In a correlated equilibrium, the players’ choice of actions is affected by random, correlated messages that they receive from an outside source, or mechanism. This allows for more equilibrium outcomes than without such messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also convey information about the types of the other players, either because they reflect extraneous events that affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Thus, mechanisms can be classified by the connections between the messages that the players receive and their own and the other players’ types, the dependence or independence of the messages, and whether randomness is involved. These properties may affect the achievable equilibrium outcomes, i.e., the payoffs and joint distributions of type and action profiles. Whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the number is 14–15 for correlated equilibria and 15–17 for communication equilibria. Each class is characterized by the properties of the mechanisms that implement its members. The majority of these classes have not been described before.Correlated equilibrium, Communication equilibrium, Incomplete information, Bayesian games, Mechanism, Correlation device, Implementation

Weighted Congestion Games With Separable Preferences

Players in a congestion game may differ from one another in their intrinsic preferences (e.g., the benefit they get from using a specific resource), their contribution to congestion, or both. In many cases of interest, intrinsic preferences and the negative effect of congestion are (additively or multiplicatively) separable. This paper considers the implications of separability for the existence of pure-strategy Nash equilibrium and the prospects of spontaneous convergence to equilibrium. It is shown that these properties may or may not be guaranteed, depending on the exact nature of player heterogeneity.congestion games, separable preferences, pure equilibrium, finite improvement property, potential.

Comparative Statics of Altruism and Spite

The equilibrium outcome of a strategic interaction between two or more people may depend on the weight they place on each other’s payoff. A positive, negative or zero weight represents altruism, spite or complete selfishness, respectively. Paradoxically, the real, material payoff in equilibrium for a group of altruists may be lower than for selfish or spiteful groups. However, this can only be so if the equilibria involved are unstable. If they are stable, the total (equivalently, average) payoff can only increase or remain unchanged with an increasing degree of altruism.Altruism, spite, comparative statics, strategic games, stability of equilibrium

Static Stability in Games

Static stability of equilibrium in strategic games differs from dynamic stability in not being linked to any particular dynamical system. In other words, it does not make any assumptions about off-equilibrium behavior. Examples of static notions of stability include evolutionarily stable strategy (ESS) and continuously stable strategy (CSS), both of which are meaningful or justifiable only for particular classes of games, namely, symmetric multilinear games or symmetric games with a unidimensional strategy space, respectively. This paper presents a general notion of local static stability, of which the above two are essentially special cases. It is applicable to virtually all n-person strategic games, both symmetric and asymmetric, with non-discrete strategy spaces.Stability of equilibrium, static stability

Network Topology and Equilibrium Existence in Weighted Network Congestion Games

Every finite noncooperative game can be presented as a weighted network congestion game, and also as a network congestion game with player-specific costs. In the first presentation, different players may contribute differently to congestion, and in the second, they are differently (negatively) affected by it. This paper shows that the topology of the underlying (undirected two-terminal) network provides information about the existence of pure-strategy Nash equilibrium in the game. For some networks, but not for others, every corresponding game has at least one such equilibrium. For the weighted presentation, a complete characterization of the networks with this property is given. The necessary and sufficient condition is that the network has at most three routes that do traverse any edge in opposite directions, or it consists of several such networks connected in series. The corresponding problem for player-specific costs remains open.Congestion games, network topology, existence of equilibrium

Random-Player Games

This paper introduces games of incomplete information in which the number, as well as the identity, of the participating players is determined by chance. The participation of certian players may not be independent of the participation of others, and hence the very fact that a particular player was chosen to play may give that player a clue as to the number and the identity of the other players chosen. However, players have to choose their strategies before the identity of the other players is fully revealed to them and thus, effectively, before they know whether or not they will take part in the game. Pure-strategy, mix-strategy, and correlated equilibria of random-player games are defined. These definitions extend the corresponding definitions for finite games, Bayesian games with consistent beliefs, and Poisson games-all of which can be seen as special cases of random-player games. Sufficient conditions for the existence of pure and mixed-strategy equilibria are given.