scholarly journals Modeling Precomputation In Games Played Under Computational Constraints

2021 ◽  
Author(s):  
Thomas Orton
Keyword(s):  
Nash Equilibrium ◽  
Numerical Experiments ◽  
Efficient Algorithms ◽  
Trade Off ◽  
Constrained Games ◽  
Novel Model ◽  
Chess Playing

Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such as chess? This paper presents a novel model for the precomputation (preparing moves in advance) aspect of computationally constrained games. A fundamental trade-off is shown between randomness of play, and susceptibility to precomputation, suggesting that randomization is necessary in games with computational constraints. We present efficient algorithms for computing how susceptible a strategy is to precomputation, and computing an $\epsilon$-Nash equilibrium of our model. Numerical experiments measuring the trade-off between randomness and precomputation are provided for Stockfish (a well-known chess playing algorithm).

scholarly journals Efficiency and Equilibrium in Network Games: An Experiment

2021 ◽  
pp. 1-44
Author(s):  
Edoardo Gallo ◽  
Chang Yan
Keyword(s):  
Nash Equilibrium ◽  
Network Structure ◽  
Economic Systems ◽  
Central Feature ◽  
Network Games ◽  
Trade Off ◽  
Network Game ◽  
Asymmetric Networks ◽  
Unique Nash Equilibrium

Abstract The tension between efficiency and equilibrium is a central feature of economic systems. We examine this trade-off in a network game with a unique Nash equilibrium in which agents can achieve a higher payoff by following a “collaborative norm”. Subjects establish and maintain a collaborative norm in the circle, but the norm weakens with the introduction of one hub connected to everyone in the wheel. In complex and asymmetric networks of 15 and 21 nodes, the norm disappears and subjects’ play converges to Nash. We provide evidence that subjects base their decisions on their degree, rather than the overall network structure.

A Novel Model and Method Based on Nash Equilibrium for Medical Image Segmentation

2018 ◽  
Vol 8 (5) ◽  
pp. 872-880
Author(s):  
Tian Chi Zhang ◽  
Jing Zhang ◽  
Jian Pei Zhang ◽  
Melvyn L. Smith ◽  
Edwin R. Hancock
Keyword(s):  
Image Segmentation ◽  
Nash Equilibrium ◽  
Medical Image ◽  
Medical Image Segmentation ◽  
Novel Model

scholarly journals Convex generalized Nash equilibrium problems and polynomial optimization

2021 ◽  
Author(s):  
Jiawang Nie ◽  
Xindong Tang
Keyword(s):  
Nash Equilibrium ◽  
Numerical Experiments ◽  
Nash Equilibria ◽  
Equilibrium Problems ◽  
Polynomial Optimization ◽  
Generalized Nash Equilibrium ◽  
Semidefinite Relaxations ◽  
The Moment ◽  
Generalized Nash Equilibria ◽  
Generalized Nash Equilibrium Problems

AbstractThis paper studies convex generalized Nash equilibrium problems that are given by polynomials. We use rational and parametric expressions for Lagrange multipliers to formulate efficient polynomial optimization for computing generalized Nash equilibria (GNEs). The Moment-SOS hierarchy of semidefinite relaxations are used to solve the polynomial optimization. Under some general assumptions, we prove the method can find a GNE if there exists one, or detect nonexistence of GNEs. Numerical experiments are presented to show the efficiency of the method.

scholarly journals Efficient algorithms for solving the p-Laplacian in polynomial time

2020 ◽  
Vol 146 (2) ◽  
pp. 369-400
Author(s):  
Sébastien Loisel
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Polynomial Time ◽  
Numerical Experiments ◽  
Nonlinear Partial Differential Equation ◽  
Numerical Algorithms ◽  
Efficient Algorithms ◽  
Barrier Method ◽  
Newton Iterations ◽  
Grid Points

Abstract The p-Laplacian is a nonlinear partial differential equation, parametrized by $$p \in [1,\infty ]$$ p ∈ [ 1 , ∞ ] . We provide new numerical algorithms, based on the barrier method, for solving the p-Laplacian numerically in $$O(\sqrt{n}\log n)$$ O ( n log n ) Newton iterations for all $$p \in [1,\infty ]$$ p ∈ [ 1 , ∞ ] , where n is the number of grid points. We confirm our estimates with numerical experiments.

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 On some general scheme of constructing iterative methods for searching the Nash equilibrium in concave games

2021 ◽  
Vol 13 (3) ◽  
pp. 75-121
Author(s):  
Андрей Владимирович Чернов ◽  
Andrey Chernov
Keyword(s):  
Nash Equilibrium ◽  
Iterative Process ◽  
Numerical Experiments ◽  
General Scheme ◽  
Iterative Algorithms ◽  
Specific Character ◽  
Residual Function ◽  
Arbitrary Continuous Function ◽  
Finite Dimensional ◽  
The Subject

The subject of the paper is finite-dimensional concave games id est noncooperative $n$-person games with objective functionals concave with respect to `their own' variables. For such games we investigate the problem of designing iterative algorithms for searching the Nash equilibrium with convergence guaranteed without requirements concerning objective functionals such as smoothness and as convexity in `strange' variables or another similar hypotheses (in the sense of weak convexity, quasiconvexity and so on). In fact, we prove some assertion analogous to the theorem on convergence of $M$-Fej\'{er iterative process for the case when an operator acts in a finite-dimensional compact and nearness to an objective set is measured with the help of arbitrary continuous function. Then, on the base of this assertion we generalize and develop the approach suggested by the author formerly to searching the Nash equilibrium in concave games. The last one can be regarded as "a cross between" the relaxation algorithm and the Hooke-Jeeves method of configurations (but taking into account a specific character of the the residual function being minimized). Moreover, we present results of numerical experiments with their discussion.

A REFINEMENT CONCEPT FOR EQUILIBRIA IN MULTICRITERIA GAMES VIA STABLE SCALARIZATIONS

2007 ◽  
Vol 09 (02) ◽  
pp. 169-181 ◽  
Author(s):  
GIUSEPPE DE MARCO ◽  
JACQUELINE MORGAN
Keyword(s):  
Nash Equilibrium ◽  
Existence Theorem ◽  
Stable Equilibrium ◽  
Multicriteria Games ◽  
Trade Off ◽  
Multicriteria Game

In a finite multicriteria game, one or more systems of weights might be implicitly used by the agents by playing a Nash equilibrium of the corresponding trade-off scalar games. In this paper, we present a refinement concept for equilibria in finite multicriteria games, called scalarization-stable equilibrium, that selects equilibria stable with respect to perturbations on the scalarization. An existence theorem is provided together with some illustrative examples and connections with some other refinement concepts are investigated.

Existence of Nash equilibrium for chance-constrained games

2016 ◽  
Vol 44 (5) ◽  
pp. 640-644 ◽  
Author(s):  
Vikas Vikram Singh ◽  
Oualid Jouini ◽  
Abdel Lisser
Keyword(s):  
Nash Equilibrium ◽  
Constrained Games

Continuous-time distributed Nash equilibrium seeking algorithms for non-cooperative constrained games

Automatica ◽  
2021 ◽  
Vol 127 ◽  
pp. 109535
Author(s):  
Yao Zou ◽  
Bomin Huang ◽  
Ziyang Meng ◽  
Wei Ren
Keyword(s):  
Nash Equilibrium ◽  
Continuous Time ◽  
Constrained Games
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