How do Tom and Jerry Play? A Simple Application of Convex Geometry in Game Theory

76 Pages Posted: 24 Jan 2022 Last revised: 30 Jan 2024

See all articles by Xinmi Li

Xinmi Li

Tsinghua University - Department of Physics

Jie Zheng

Shandong University - Center for Economic Research

Date Written: January 18, 2022

Abstract

We propose a simultaneous-move hide-and-seek game, where one player wins by matching the other player, while the other player wins by mismatching in a connected space X in Euclidean space. We provide a complete characterization of Type I Nash Equilibrium where the seeker plays a pure strategy. We show that the center of mass of the hider’s strategy coincides with the seeker’s strategy at the center of the minimal cover ball of X. We also characterize Type II Nash Equilibrium where both players randomize their strategies. We show that the shape of X matters and the players only allocate their probability weights along a straight line. Some alternative settings are discussed and the equilibrium analysis is conducted. These results can be applied to a large number of scenarios, characterizing the behavior of two players in a zero-sum game, where one player aims to maximize the distance between them, while the other aims to minimize it.

Keywords: Hide and Seek, Simultaneous-move Game, Zero-sum Game, Convex Geometry, Nash Equilibrium

JEL Classification: C72

Suggested Citation

Li, Xinmi and Zheng, Jie, How do Tom and Jerry Play? A Simple Application of Convex Geometry in Game Theory (January 18, 2022). Available at SSRN: https://ssrn.com/abstract=4001491 or http://dx.doi.org/10.2139/ssrn.4001491

Xinmi Li (Contact Author)

Tsinghua University - Department of Physics ( email )

Beijing, Beijing 100084
China

Jie Zheng

Shandong University - Center for Economic Research ( email )

Jinan, Shandong 250100
China

HOME PAGE: http://https://meetecon.com/jie/

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