Nash Equilibria on (Un)Stable Networks

Anton Badev

doi:10.3982/ecta12576

Nash Equilibria on (Un)Stable Networks

Econometrica ◽

10.3982/ecta12576 ◽

2021 ◽

Vol 89 (3) ◽

pp. 1179-1206

Author(s):

Anton Badev

Keyword(s):

High Schools ◽

Bounded Rationality ◽

Nash Equilibria ◽

Smoking Prevalence ◽

Optimal Strategies ◽

Friendship Network ◽

Price Changes ◽

Peer Effect ◽

Racial Desegregation ◽

Intended Effect

In response to a change, individuals may choose to follow the responses of their friends or, alternatively, to change their friends. To model these decisions, consider a game where players choose their behaviors and friendships. In equilibrium, players internalize the need for consensus in forming friendships and choose their optimal strategies on subsets of k players—a form of bounded rationality. The k‐player consensual dynamic delivers a probabilistic ranking of a game's equilibria, and via a varying k, facilitates estimation of such games. Applying the model to adolescents' smoking suggests that: (a) the response of the friendship network to changes in tobacco price amplifies the intended effect of price changes on smoking, (b) racial desegregation of high schools decreases the overall smoking prevalence, (c) peer effect complementarities are substantially stronger between smokers compared to between nonsmokers.

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On the existence of stationary Nash equilibria in average stochastic games with finite state and action spaces

Contributions to Game Theory and Management ◽

10.21638/11701/spbu31.2020.16 ◽

2020 ◽

Vol 13 ◽

pp. 304-323

Author(s):

Dmitrii Lozovanu ◽

◽

Stefan Pickl ◽

Keyword(s):

Nash Equilibria ◽

Stochastic Games ◽

Optimal Strategies ◽

Stationary Strategies ◽

Finite State ◽

Optimal Stationary Strategies ◽

Action Spaces

We consider infinite n-person stochastic games with limiting average payoffs criteria for the players. The main results of the paper are concerned with the existence of stationary Nash equilibria and determining the optimal strategies of the players in the games with finite state and action spaces. We present conditions for the existence of stationary Nash equilibria in the considered games and propose an approach for determining the optimal stationary strategies of the players if such strategies exist.

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On Optimal Antijamming Strategies in Sensor Networks

International Journal of Distributed Sensor Networks ◽

10.1155/2012/793194 ◽

2012 ◽

Vol 8 (4) ◽

pp. 793194

Author(s):

Yanmin Zhu ◽

Yuan Jiang

Keyword(s):

Sensor Networks ◽

Sensor Network ◽

Nash Equilibria ◽

Optimal Strategies ◽

Wireless Channel ◽

Wireless Sensor ◽

Security Threat ◽

Pareto Dominance ◽

Jamming Attacks ◽

Risk Dominance

Physical layer radio jamming is a serious security threat to a wireless sensor network since the network relies on open wireless radio channels. A radio jammer is typically strategic and chooses its jamming strategy in response to the possible defense strategy taken by the sensor network. In this paper we model the interaction between the sensor network and the attacker as a noncooperative nonzero-sum static game. In such a game, the sensor network has a set of strategies of controlling its probability of wireless channel access and the attacker manipulates its jamming by controlling its jamming probability after sensing a transmission activity. We propose an algorithm for computing the optimal strategies for jamming attack and network defense. A critical issue is that there may exist a number of possible strategy profiles of Nash equilibria. To address this issue, we further propose to choose realistic Nash equilibria by applying the Pareto dominance and risk dominance. Our numerical results demonstrate that the strategies chosen by the Pareto dominance and risk dominance achieve the expected performance. Our results presented in the paper provide valuable defense guidance for wireless sensor networks against jamming attacks.

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On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games

International Game Theory Review ◽

10.1142/s0219198918400017 ◽

2018 ◽

Vol 20 (03) ◽

pp. 1840001

Author(s):

Stefanos Leonardos ◽

Costis Melolidakis

Keyword(s):

Nash Equilibrium ◽

Nash Equilibria ◽

Sufficient Conditions ◽

Solution Concept ◽

Optimal Strategies ◽

Payoff Matrix ◽

Matrix Game ◽

Bimatrix Games ◽

Equilibrium Payoff ◽

The Relationship

Given a bimatrix game, the associated leadership or commitment games are defined as the games at which one player, the leader, commits to a (possibly mixed) strategy and the other player, the follower, chooses his strategy after being informed of the irrevocable commitment of the leader (but not of its realization in case it is mixed). Based on a result by Von Stengel and Zamir [2010], the notions of commitment value and commitment optimal strategies for each player are discussed as a possible solution concept. It is shown that in nondegenerate bimatrix games (a) pure commitment optimal strategies together with the follower’s best response constitute Nash equilibria, and (b) strategies that participate in a completely mixed Nash equilibrium are strictly worse than commitment optimal strategies, provided they are not matrix game optimal. For various classes of bimatrix games that generalize zero-sum games, the relationship between the maximin value of the leader’s payoff matrix, the Nash equilibrium payoff and the commitment optimal value are discussed. For the Traveler’s Dilemma, the commitment optimal strategy and commitment value for the leader are evaluated and seem more acceptable as a solution than the unique Nash equilibrium. Finally, the relationship between commitment optimal strategies and Nash equilibria in [Formula: see text] bimatrix games is thoroughly examined and in addition, necessary and sufficient conditions for the follower to be worse off at the equilibrium of the leadership game than at any Nash equilibrium of the simultaneous move game are provided.

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