scholarly journals Renegotiation Perfection in Infinite Games

Game Theory ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Julian C. Jamison
Keyword(s):  
Solution Concept ◽  
Dynamic Structure ◽  
Infinite Games ◽  
Welfare Gains ◽  
Extensive Form ◽  
Finite Games ◽  
Perfect Set ◽  
Extensive Form Game ◽  
Covering Set ◽  
Definition Of

We study the dynamic structure of equilibria in game theory. Allowing players in a game the opportunity to renegotiate, or switch to a feasible and Pareto superior equilibrium, can lead to welfare gains. However, in an extensive-form game this can also make it more difficult to enforce punishment strategies, leading to the question of which equilibria are feasible after all. This paper attempts to resolve that question by presenting the first definition of renegotiation-proofness in general games. This new concept, the renegotiation perfect set, satisfies five axioms. The first three axioms—namely Rationality, Consistency, and Internal Stability—characterize weakly renegotiation-proof sets. There is a natural generalized tournament defined on the class of all WRP sets, and the final two axioms—External Stability and Optimality—pick a unique “winner” from this tournament. The tournament solution concept employed, termed the catalog, is based on Dutta’s minimal covering set and can be applied to many settings other than renegotiation. It is shown that the renegotiation perfection concept is an extension of the standard renegotiation-proof definition for finite games, introduced by (Benoit and Krishna 1993), and that it captures the notion of a strongly renegotiation-proof equilibrium as defined by (Farrell and Maskin 1989).

scholarly journals When to Follow the Tip: Security Games with Strategic Informants

2020 ◽  
Author(s):  
Weiran Shen ◽  
Weizhe Chen ◽  
Taoan Huang ◽  
Rohit Singh ◽  
Fei Fang
Keyword(s):  
Solution Concept ◽  
Extensive Form ◽  
Research Attention ◽  
The Past ◽  
Bayesian Equilibrium ◽  
Strategic Behaviors ◽  
Security Games ◽  
Extensive Form Game ◽  
Patrol Strategies ◽  
Security Game

Although security games have attracted intensive research attention over the past years, few existing works consider how information from local communities would affect the game. In this paper, we introduce a new player -- a strategic informant, who can observe and report upcoming attacks -- to the defender-attacker security game setting. Characterized by a private type, the informant has his utility structure that leads to his strategic behaviors. We model the game as a 3-player extensive-form game and propose a novel solution concept of Strong Stackelberg-perfect Bayesian equilibrium. To compute the optimal defender strategy, we first show that although the informant can have infinitely many types in general, the optimal defense plan can only include a finite (exponential) number of different patrol strategies. We then prove that there exists a defense plan with only a linear number of patrol strategies that achieve the optimal defender's utility, which significantly reduces the computational burden and allows us to solve the game in polynomial time using linear programming. Finally, we conduct extensive experiments to show the effect of the strategic informant and demonstrate the effectiveness of our algorithm.

scholarly journals Monty Hall three door ’anomaly’ revisited: a note on deferment in an extensive form game

2021 ◽  
Author(s):  
Philipp E. Otto
Keyword(s):  
Probability Theory ◽  
Decision Problems ◽  
Extensive Form ◽  
Form Game ◽  
Information Updating ◽  
Extensive Form Game ◽  
Monty Hall ◽  
Initial Choice

AbstractThe Monty Hall game is one of the most discussed decision problems, but where a convincing behavioral explanation of the systematic deviations from probability theory is still lacking. Most people not changing their initial choice, when this is beneficial under information updating, demands further explanation. Not only trust and the incentive of interestingly prolonging the game for the audience can explain this kind of behavior, but the strategic setting can be modeled more sophisticatedly. When aiming to increase the odds of winning, while Monty’s incentives are unknown, then not to switch doors can be considered as the most secure strategy and avoids a sure loss when Monty’s guiding aim is not to give away the prize. Understanding and modeling the Monty Hall game can be regarded as an ideal teaching example for fundamental statistic understandings.

Game Theory and Security Studies

2019 ◽  
pp. 7-24
Author(s):  
Frank C. Zagare
Keyword(s):  
Game Theory ◽  
Short Review ◽  
Dominant Strategy ◽  
Security Studies ◽  
Form Game ◽  
Bayesian Equilibrium ◽  
Subgame Perfection ◽  
Extensive Form Game ◽  
The Many ◽  
Definition Of

This chapter describes the basic assumptions of game theory and illustrates its major concepts, using examples drawn from the security studies literature. An arms race game is used as an example of a strategic form game, illustrating the meaning of an equilibrium outcome and the definition of a dominant strategy. Backward induction and the definition of subgame perfection are explained in the context of an extensive form game that features threats. Nash equilibrium and the Bayesian equilibrium are discussed, and a short review of the many applications of game theory in international politics is provided. Finally, the chapter concludes with a discussion of the usefulness of game theory in generating insights about deterrence.

scholarly journals Quasi-Perfect Stackelberg Equilibrium

2019 ◽  
Vol 33 ◽  
pp. 2117-2124 ◽  
Author(s):  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Christian Kroer ◽  
Nicola Gatti ◽  
Tuomas Sandholm
Keyword(s):  
Broad Class ◽  
Stackelberg Equilibrium ◽  
Correlated Equilibrium ◽  
Equilibrium Concept ◽  
Extensive Form ◽  
Tree Form ◽  
Axiomatic Definition ◽  
Security Games ◽  
Definition Of ◽  
Perfect Equilibria

Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasiperfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings—that is, settings where a leader can commit to a strategy—which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes.

scholarly journals Solving Large Extensive-Form Games with Strategy Constraints

2019 ◽  
Vol 33 ◽  
pp. 1861-1868
Author(s):  
Trevor Davis ◽  
Kevin Waugh ◽  
Michael Bowling
Keyword(s):  
Private Information ◽  
Imperfect Information ◽  
Risk Mitigation ◽  
Solution Concept ◽  
Optimal Strategies ◽  
Linear Constraints ◽  
Convex Constraints ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Large Extensive Form Games

Extensive-form games are a common model for multiagent interactions with imperfect information. In two-player zerosum games, the typical solution concept is a Nash equilibrium over the unconstrained strategy set for each player. In many situations, however, we would like to constrain the set of possible strategies. For example, constraints are a natural way to model limited resources, risk mitigation, safety, consistency with past observations of behavior, or other secondary objectives for an agent. In small games, optimal strategies under linear constraints can be found by solving a linear program; however, state-of-the-art algorithms for solving large games cannot handle general constraints. In this work we introduce a generalized form of Counterfactual Regret Minimization that provably finds optimal strategies under any feasible set of convex constraints. We demonstrate the effectiveness of our algorithm for finding strategies that mitigate risk in security games, and for opponent modeling in poker games when given only partial observations of private information.

scholarly journals Secure Degrees of Freedom in Networks with User Misbehavior

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 945
Author(s):  
Karim Banawan ◽  
Sennur Ulukus
Keyword(s):  
Secure Communication ◽  
Multiple Access ◽  
Degrees Of Freedom ◽  
Broadcast Channel ◽  
Interference Channel ◽  
Extensive Form ◽  
Wiretap Channel ◽  
Form Game ◽  
Cooperative Jamming ◽  
Extensive Form Game

We investigate the secure degrees of freedom (s.d.o.f.) of three new channel models: broadcast channel with combating helpers, interference channel with selfish users, and multiple access wiretap channel with deviating users. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. That is in contrast with the common assumption in the literature that the users follow a certain protocol altruistically and transmit both message-carrying and cooperative jamming signals in an optimum manner. In the first model, over a classical broadcast channel with confidential messages (BCCM), there are two helpers, each associated with one of the receivers. In the second model, over a classical interference channel with confidential messages (ICCM), there is a helper and users are selfish. By casting each problem as an extensive-form game and applying recursive real interference alignment, we show that, for the first model, the combating intentions of the helpers are neutralized and the full s.d.o.f. is retained; for the second model, selfishness precludes secure communication and no s.d.o.f. is achieved. In the third model, we consider the multiple access wiretap channel (MAC-WTC), where multiple legitimate users wish to have secure communication with a legitimate receiver in the presence of an eavesdropper. We consider the case when a subset of users deviate from the optimum protocol that attains the exact s.d.o.f. of this channel. We consider two kinds of deviation: when some of the users stop transmitting cooperative jamming signals, and when a user starts sending intentional jamming signals. For the first scenario, we investigate possible responses of the remaining users to counteract such deviation. For the second scenario, we use an extensive-form game formulation for the interactions of the deviating and well-behaving users. We prove that a deviating user can drive the s.d.o.f. to zero; however, the remaining users can exploit its intentional jamming signals as cooperative jamming signals against the eavesdropper and achieve an optimum s.d.o.f.

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