Equilibrium Existence and Uniqueness In Network Games with Additive Preferences

A directed network game of imperfect strategic substitutes with heterogeneous players is analyzed. We consider concave additive separable utility functions that encompass the quasi-linear ones. It is found that pure strategy Nash equilibria verify a non-linear complementarity problem. By requiring appropriate concavity in the utility functions, the existence of an equilibrium point is shown and equilibrium uniqueness is established with a P -matrix. Then, it appears that previous findings on network structure and sparsity hold for many more games

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.

Fragility of the Commons under Prospect-Theoretic Risk Attitudes

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each player's risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure Nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource. Greater competition, vis-a-vis the number of players, increases the failure probability at the Nash equilibrium; we quantify this effect by obtaining bounds on the ratio of the failure probability at the Nash equilibrium to the failure probability under investment by a single user. We further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium.Comment: Accepted for publication in Games and Economic Behavior, 201

Ambiguity and public good provision in large societies

In this paper we consider the effect of ambiguity on the private provision of public goods. Equilibrium is shown to exist and be unique. We examine how provision of the public good changes as the size of the population increases. We show that when there is uncertainty there may be less free-riding in large societies

Uniqueness Conditions for Point-Rationalizable

The unique point-rationalizable solution of a game is the unique Nash equilibrium. However, this solution has the additional advantage that it can be justified by the epistemic assumption that it is Common Knowledge of the players that only best responses are chosen. Thus, games with a unique point-rationalizable solution allow for a plausible explanation of equilibrium play in one-shot strategic situations, and it is therefore desireable to identify such games. In order to derive sufficient and necessary conditions for unique point-rationalizable solutions this paper adopts and generalizes the contraction-property approach of Moulin (1984) and of Bernheim (1984). Uniqueness results obtained in this paper are derived under fairly general assumptions such as games with arbitrary metrizable strategy sets and are especially useful for complete and bounded, for compact, as well as for finite strategy sets. As a mathematical side result existence of a unique fixed point is proved under conditions that generalize a fixed point theorem due to Edelstein (1962).

Interplay between security providers, consumers, and attackers: a weighted congestion game approach

Network users can choose among different security solutions to protect their data. Those solutions are offered by competing providers, with possibly different performance and price levels. In this paper, we model the interactions among users as a noncooperative game, with a negative externality coming from the fact that attackers target popular systems to maximize their expected gain. Using a nonatomic weighted congestion game model for user interactions, we prove the existence and uniqueness of a user equilibrium, compute the corresponding Price of Anarchy, that is the loss of efficiency due to user selfishness, and investigate some consequences for the (higher-level) pricing game played by security providers.Game theory;Weighted games; Security

How to use Rosen's normalised equilibrium to enforce a socially desirable Pareto efficient solution

We consider a situation, in which a regulator believes that constraining a complex good created jointly by competitive agents, is socially desirable. Individual levels of outputs that generate the constrained amount of the externality can be computed as a Pareto efficient solution of the agents' joint utility maximisation problem. However, generically, a Pareto efficient solution is not an equilibrium. We suggest the regulator calculates a Nash-Rosen coupled-constraint equilibrium (or a “generalised” Nash equilibrium) and uses the coupled-constraint Lagrange multiplier to formulate a threat, under which the agents will play a decoupled Nash game. An equilibrium of this game will possibly coincide with the Pareto efficient solution. We focus on situations when the constraints are saturated and examine, under which conditions a match between an equilibrium and a Pareto solution is possible. We illustrate our findings using a model for a coordination problem, in which firms' outputs depend on each other and where the output levels are important for the regulator.