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Equilibrium without independence
, 1988
"... Because players whose preferences violate the von NeumannMorgenstern independence axiom may be unwilling to randomize as mixedstrategy Nash equilibrium would require, a Nash equilibrium may not exist without independence. This paper generalizes Nash’s definition of equilibrium, retaining its ratio ..."
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Because players whose preferences violate the von NeumannMorgenstern independence axiom may be unwilling to randomize as mixedstrategy Nash equilibrium would require, a Nash equilibrium may not exist without independence. This paper generalizes Nash’s definition of equilibrium, retaining its rationalexpectations spirit but relaxing its requirement that a player must bear as much uncertainty about his own strategy choice as other players do. The resulting notion, “equilibrium in beliefs, ” is equivalent to Nash equilibrium when independence is satistied, but exists without independence. This makes it possible to study the robustness of equilibrium comparative statics results to violations of independence. Jotuna / of ’ Gononric, Lirerarurr Classification Numbers: 022, 026. ” 1990 Academic Press. inc. 1.
N.Y.: Bounded interpersonal inferences and decision making. Economic Theory (this issue
"... Summary. Individual decision making is based on predictions about other players’ choices as well as on valuations of reactions to predictions. In this sense, a player has a predictiondecision criterion for decision making. We develop a theory of predictiondecision criteria, which enables us to cap ..."
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Cited by 4 (4 self)
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Summary. Individual decision making is based on predictions about other players’ choices as well as on valuations of reactions to predictions. In this sense, a player has a predictiondecision criterion for decision making. We develop a theory of predictiondecision criteria, which enables us to capture new phenomena on individual decision making in games. The decision making situation is described in the epistemic logic GLEF of shallow depths. There, each player considers his and other players ’ decision making down to some shallow depths. It is a point of our theory to investigate inferential complexities of interpersonal introspections. In particular, we can discuss a minimal epistemic inferential structure for predictiondecision making. We will find parallel structures in decision making and prediction making, which is called an inner parallelism. The climax of the paper is the consideration of inner parallelisms of predictiondecision making.
Adversarial Leakage in Games
"... While the maximin strategy has become the standard, and most agreedupon solution for decisionmaking in adversarial settings, as discussed in game theory, computer science and other disciplines, its power arises from the use of mixed strategies, a.k.a. probabilistic algorithms. Nevertheless, in adv ..."
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Cited by 2 (1 self)
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While the maximin strategy has become the standard, and most agreedupon solution for decisionmaking in adversarial settings, as discussed in game theory, computer science and other disciplines, its power arises from the use of mixed strategies, a.k.a. probabilistic algorithms. Nevertheless, in adversarial settings we face the risk of information leakage about the actual strategy instantiation. Hence, real robust algorithms should take information leakage into account. To address this fundamental issue, we introduce the study of adversarial leakage in games. We consider two models of leakage. In both of them the adversary is able to learn the value of b binary predicates about the strategy instantiation. In one of the models these predicates are selected after the decisionmaker announces its probabilistic algorithm and in the other one they are decided in advance. We give tight results about the effects of adversarial leakage in general zerosum games with binary payoffs as a function of the level of leakage captured by b in both models. We also compare the power of adversarial leakage in the two models and the robustness of the original maximin strategies of games to adversarial leakage. Finally, we study the computation of optimal strategies for adversarial leakage models. Together, our study introduces a new framework for robust decisionmaking, and provides rigorous fundamental understanding of its properties.
Suicidal altruism under random assortment
"... Questions: Can there be a selective explanation for suicide? Or are all suicides evolutionary mistakes, ever pruned by natural selection to the extent that the tendency to perform them is heritable? Model: A simple variant of trait group selection (where a population is divided into mutually exclusi ..."
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Questions: Can there be a selective explanation for suicide? Or are all suicides evolutionary mistakes, ever pruned by natural selection to the extent that the tendency to perform them is heritable? Model: A simple variant of trait group selection (where a population is divided into mutually exclusive groups, with the direct effects of behaviour limited to groupmates), employing predators as the mechanism underlying group selection. Predators evaluate groups to avoid potentially suicidal defenders (which, when present, limit a predator’s net return), thus acting as a group selection mechanism favouring groups with potentially suicidal altruists. Conclusion: The model supports contingent strong altruism (depressing one’s direct reproduction – absolute fitness – to aid others) without kin assortment. Even an extreme contingent suicidal type (destroying self for the sake of others) may either saturate a population or be polymorphic with a type avoiding such altruism. The model does not, however, support a sterile worker caste, where sterility occurs before lifehistory events associated with effective altruism; under random assortment, reproductive suicide must remain contingent or facultative.
Regret Freedom Isn’t Free
, 2012
"... Abstract. Cooperative, peertopeer (P2P) services—distributed systems consisting of participants from multiple administrative domains (MAD)—must deal with the threat of arbitrary (Byzantine) failures while incentivizing the cooperation of potentially selfish (rational) nodes that such services rely ..."
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Abstract. Cooperative, peertopeer (P2P) services—distributed systems consisting of participants from multiple administrative domains (MAD)—must deal with the threat of arbitrary (Byzantine) failures while incentivizing the cooperation of potentially selfish (rational) nodes that such services rely on to function. This paper investigates how to specify conditions (i.e., a solution concept) for rational cooperation in an environment that also contains Byzantine and obedient peers. We find that regretfree approaches—which, inspired by traditional Byzantine fault tolerance, condition rational cooperation on identifying a strategy that proves a best response regardless of how Byzantine failures occur—are unattainable in many faulttolerant distributed systems. We suggest an alternative regretbraving approach, in which rational nodes aim to best respond to their expectations regarding Byzantine failures: the chosen strategy guarantees no regret only to the extent that such expectations prove correct. While work on regretbraving solution concepts is just beginning, our preliminary results show that these solution concepts are not subject to the fundamental limitations inherent to regret freedom. 1
Maximin Play in TwoPerson
"... VITALY PRUZHANSKY Abstract. Since the seminal paper of Nash [7] game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. We study the properties of these strategies in 2player nonzerosum strategic games, whose Nash equilibria are only mixed. 1. ..."
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VITALY PRUZHANSKY Abstract. Since the seminal paper of Nash [7] game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. We study the properties of these strategies in 2player nonzerosum strategic games, whose Nash equilibria are only mixed. 1.
SUBJECJWITY AND CORRELATION IN RANDOMIZED STRATEGIES*
, 1973
"... Subjectivity and correlation, though formally related, are conceptually distinct and independent issues. We start by discussing subjectivity. A mixed strategy in a game involves the selection of a pure strategy by means of a random device. It has usually been assumed that the random device is a ..."
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Subjectivity and correlation, though formally related, are conceptually distinct and independent issues. We start by discussing subjectivity. A mixed strategy in a game involves the selection of a pure strategy by means of a random device. It has usually been assumed that the random device is a
Man versus Nash An experiment on the selfenforcing nature of mixed strategy equilibrium
, 2011
"... We examine experimentally how humans behave when they play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zerosum and another unprofitable with a pure minimax strategy. A minority of subjects ’ play was consistent with their Nash equili ..."
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We examine experimentally how humans behave when they play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zerosum and another unprofitable with a pure minimax strategy. A minority of subjects ’ play was consistent with their Nash equilibrium strategy, while a larger percentage of subjects ’ play was more consistent with different models of play: equiprobable play for the zerosum game, and the minimax strategy in the unprofitable game. We estimate the heterogeneity and dynamics of the subjects ’ latent mixed strategy sequences via a hidden Markov model. This provides clear results on the identification of the use of pure and mixed strategies and the limiting distribution over strategies. The mixed strategy Nash equilibrium is not selfenforcing except when it coincides with the equal probability mixed strategy, and there is surprising amounts of pure strategy play and clear cycling between the pure strategy states.
c ○ 2013 Society for Industrial and Applied Mathematics ADVERSARIAL LEAKAGE IN GAMES ∗
"... Abstract. While the minimax (or maximin) strategy has become the standard and most agreedupon solution for decision making in adversarial settings, as discussed in game theory, computer science, and other disciplines, its power arises from the use of mixed strategies, also known as probabilistic alg ..."
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Abstract. While the minimax (or maximin) strategy has become the standard and most agreedupon solution for decision making in adversarial settings, as discussed in game theory, computer science, and other disciplines, its power arises from the use of mixed strategies, also known as probabilistic algorithms. Nevertheless, in adversarial settings we face the risk of information leakage about the actual strategy instantiation. Hence, real robust algorithms should take information leakage into account. In this paper we introduce the notion of adversarial leakage in games, namely, the ability of a player to learn the value of b binary predicates about the strategy instantiation of her opponent. Different leakage models are suggested and tight bounds on the effect of adversarial leakage as a function of the level of leakage (captured by b) are established. The complexity of computing optimal strategies under these adversarial leakage models is also addressed. Together, our study introduces a new framework for robust decision making and provides rigorous fundamental understanding of its properties.