scholarly journals Last minute panic in zero sum games

2019 ◽  
Vol 25 ◽  
pp. 25
Author(s):  
Stefan Ankirchner ◽  
Christophette Blanchet-Scalliet ◽  
Kai Kümmel
Keyword(s):  
Nash Equilibrium ◽  
Theoretical Model ◽  
Unique Solution ◽  
Numerical Experiments ◽  
Strong Impact ◽  
Isaacs Equation ◽  
Sports Teams ◽  
Zero Sum Games ◽  
Set Up ◽  
Zero Sum

We set up a game theoretical model to analyze the optimal attacking intensity of sports teams during a game. We suppose that two teams can dynamically choose among more or less offensive actions and that the scoring probability of each team depends on both teams’ actions. We assume a zero sum setting and characterize a Nash equilibrium in terms of the unique solution of an Isaacs equation. We present results from numerical experiments showing that a change in the score has a strong impact on strategies, but not necessarily on scoring intensities. We give examples where strategies strongly depend on the score, the scoring intensities not at all.

scholarly journals Random Actions in Experimental Zero-Sum Games

2021 ◽  
Vol 13 (1(J)) ◽  
pp. 69-81
Author(s):  
Jung S. You
Keyword(s):  
Nash Equilibrium ◽  
Mixed Strategy ◽  
Theoretical Models ◽  
Zero Sum Games ◽  
Strategy Equilibrium ◽  
Mixed Strategy Nash Equilibrium ◽  
Matching Pennies ◽  
Business Politics ◽  
The Game Theory ◽  
Zero Sum

A mixed strategy, a strategy of unpredictable actions, is applicable to business, politics, and sports. Playing mixed strategies, however, poses a challenge, as the game theory involves calculating probabilities and executing random actions. I test i.i.d. hypotheses of the mixed strategy Nash equilibrium with the simplest experiments in which student participants play zero-sum games in multiple iterations and possibly figure out the optimal mixed strategy (equilibrium) through the games. My results confirm that most players behave differently from the Nash equilibrium prediction for the simplest 2x2 zero-sum game (matching-pennies) and 3x3 zero-sum game (e.g., the rock-paper-scissors game). The results indicate the need to further develop theoretical models that explain a non-Nash equilibrium behavior.

scholarly journals Justifying optimal play via consistency

2019 ◽  
Vol 14 (4) ◽  
pp. 1185-1201
Author(s):  
Florian Brandl ◽  
Felix Brandt
Keyword(s):  
Nash Equilibrium ◽  
Minimax Theorem ◽  
Bimatrix Games ◽  
Zero Sum Games ◽  
Zero Sum ◽  
Normative Foundations ◽  
Coherent Behavior

Developing normative foundations for optimal play in two‐player zero‐sum games has turned out to be surprisingly difficult, despite the powerful strategic implications of the minimax theorem. We characterize maximin strategies by postulating coherent behavior in varying games. The first axiom, called consequentialism, states that how probability is distributed among completely indistinguishable actions is irrelevant. The second axiom, consistency, demands that strategies that are optimal in two different games should still be optimal when there is uncertainty regarding which of the two games will actually be played. Finally, we impose a very mild rationality assumption, which merely requires that strictly dominated actions will not be played. Our characterization shows that a rational and consistent consequentialist who ascribes the same properties to his opponent has to play maximin strategies. This result can be extended to characterize Nash equilibrium in bimatrix games whenever the set of equilibria is interchangeable.

scholarly journals Nash Equilibrium Computation in Subnetwork Zero-Sum Games With Switching Communications

2016 ◽  
Vol 61 (10) ◽  
pp. 2920-2935 ◽  
Author(s):  
Youcheng Lou ◽  
Yiguang Hong ◽  
Lihua Xie ◽  
Guodong Shi ◽  
Karl Henrik Johansson
Keyword(s):  
Nash Equilibrium ◽  
Zero Sum Games ◽  
Equilibrium Computation ◽  
Zero Sum

How Risky is it to Deviate from Nash Equilibrium?

2016 ◽  
Vol 18 (03) ◽  
pp. 1650006 ◽  
Author(s):  
Irit Nowik
Keyword(s):  
Nash Equilibrium ◽  
Risk Measures ◽  
Risk Measure ◽  
Matrix Game ◽  
Integer Programming Problem ◽  
Zero Sum Games ◽  
Potential Damage ◽  
Zero Sum ◽  
S Model ◽  
Special Case

The purpose of this work is to offer for each player and any Nash equilibrium (NE), a measure for the potential risk in deviating from the NE strategy in any two person matrix game. We present two approaches regarding the nature of deviations: Strategic and Accidental. Accordingly, we define two models: S-model and T-model. The S-model defines a new game in which players deviate in the least dangerous direction. The risk defined in the T-model can serve as a refinement for the notion of “trembling hand perfect equilibrium” introduced by R. Selten. The risk measures enable testing and evaluating predictions on the behavior of players. For example: do players deviate more from a NE that is less risky? This may be relevant to the design of experiments. We present an Integer programming problem that computes the risk for any given player and NE. In the special case of zero-sum games with a unique strictly mixed NE, we prove that the risks of the players always coincide, even if the game is far from symmetry. This result holds for any norm we use for the size of deviations. We compare our risk measures to the risk measure defined by Harsanyi and Selten which is based on criteria of stability rather than on potential damage. We show that the measures may contradict.

Two-Player Non-Zero-Sum Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Nash Equilibrium ◽  
Security Policy ◽  
The Other ◽  
Bimatrix Games ◽  
Zero Sum Games ◽  
Best Response ◽  
Key Concepts ◽  
Player Game ◽  
Zero Sum ◽  
Action Spaces

This chapter defines a number of key concepts for non-zero-sum games involving two players. It begins by considering a two-player game G in which two players P₁ and P₂ are allowed to select policies within action spaces Γ‎₁ and Γ‎₂, respectively. Each player wants to minimize their own outcome, and does not care about the outcome of the other player. The chapter proceeds by discussing the security policy and Nash equilibrium for two-player non-zero-sum games, bimatrix games, admissible Nash equilibrium, and mixed policy. It also explores the order interchangeability property for Nash equilibria in best-response equivalent games before concluding with practice exercises and their corresponding solutions, along with additional exercises.

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