A Survey of Decision Making in Adversarial Games

Abstract

Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner, but without obvious malice to other players. However, in many practical applications, such as poker, chess, evader pursuing, drug interdiction, coast guard, cyber-security, and national defense, players often have apparently adversarial stances, that is, selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Along this line, this paper provides a systematic survey on three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

Linear Last-Iterate Convergence for Continuous Games with Coupled Inequality Constraints

“…one has that (22) holds by (5). Consequently, it remains to prove that there exists y * satisfying (20).…”

“…Choose Q i to be a diagonal matrix. For each i ∈ [N ], randomly select the diagonals of Q i , b i , L i and w i from [1,8], [1,2], [10,20], [1,3] and [5,10] with uniform distributions, respectively. The communication graph is randomly created as shown in Fig.…”

“…Assume that the variational GNE x * and the global dual variable λ * are given, which satisfy (4) and (5)…”

“…A principal concept in noncooperative games is Nash equilibrium (NE), representing a stable and desirable state from which no one has incentive to deviate. The types of convergence involved in existing NE seeking algorithms can be classified into the empirical distribution (i.e., timeaverage) of no-regret play and day-to-day play (i.e., last-iterate convergence) [5]. In general, a no-regret learning algorithm can achieve sublinear regret bounds and generally ensure the convergence in the sense of empirical distribution, while may often fail to guarantee the last-iterate convergence, except for quite a few scenarios, such as two-player zero-sum games [6].…”