THE POWER OF KNOWLEDGE IN GAMES

It is important to study game algorithms and resource allocation strategies in the security field with the increasing number of unconventional emergencies, complexity and destructiveness. This paper introduces the current research status of game algorithms and resource allocation algorithms in the security field, analyzes the solution algorithms and models involved in detail, and evaluates the existing problems and application values objectively in order to play a certain reference role for similar research. At present, game algorithms in the security field are mainly divided into four categories: noncooperative games, cooperative games, complete information games, and incomplete information games. The most typical noncooperative game is Stackelberg game, Shapley value method is a common model solving algorithm in cooperative game. The complete information game uses the genetic algorithm to solve the event’s Nash equilibrium solution. The incomplete information game uses the Harsanyi transformation to transform the incomplete information into the probability distribution for the solution. Therefore, errors are indispensable when constructing game models. In resource allocation, the DEA model, ant colony algorithm and HTN-based planning method can be improved to improve the emergency capacity and reduce losses.

An agent, or a coalition of agents, faces an ethical dilemma between several statements if she is forced to make a conscious choice between which of these statements will be true. This paper proposes to capture ethical dilemmas as a modality in strategic game settings with and without limit on sacrifice and for perfect and imperfect information games. The authors show that the dilemma modality cannot be defined through the earlier proposed blameworthiness modality. The main technical result is a sound and complete axiomatization of the properties of this modality with sacrifice in games with perfect information.

This article analyses the strategic moves of governments and investors under privatization programs in a game‐theoretic context. In sequential‐move games of both perfect information and incomplete information, the best response of the strategic investors to observing a slow pace of privatization is to have a low participation in economic activity because of concerns over public policy credibility. This is true even if the government chooses to randomize its action to send mixed signals to the investors while adopting a slow pace of privatization for budgetary reasons. However, the outcome is Pareto inferior to a situation of phased but fast implementation of privatization programs and high private‐sector participation under plausible assumptions. Copyright © 2011 John Wiley & Sons, Ltd.

Nonlinear dynamics of discrete time multi-level leader–follower games

Bargaining with Learning

Given an agent with limited sensing capabilities, we analyze whether it is possible to deploy a new agent in the operational space of the preexisting agent in a safe manner. One approach for modeling the interaction of the introduced agent with its environment, which contains the preexisting agent, is through a two-player game of imperfect information. However, the computational cost of solving this game is prohibitive. Restricting the preexisting agent's strategy to just memoryless strategies and assuming that the introduced agent has perfect information alleviates the computational cost while still modeling realistic environments. The proposed algorithm for solving the game finds a winning strategy for the introduced agent by solving a quantified Boolean formula (QBF) for the game. We justify this approach by establishing a matching PSPACE lower bound. We also show that this result holds even when the preexisting agent uses bounded history to condition its play.

Revisiting games of incomplete information with analogy-based expectations

This chapter presents the concept of a Bayesian Nash equilibrium as defined by Harsanyi (1967). His approach was to transform a game of incomplete information into one of imperfect information; any buyer who has incomplete information about other buyers’ values is treated as if he were uncertain about their types. A brief introduction to auctions is provided, and how these can be viewed as games of incomplete information is explained. The notations that will be used throughout the book are defined.

We characterize three interrelated solution concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model in a framework with incomplete information. Based on it, we give two groups of conditions; one characterizes permissibility and proper rationalizability, the other characterizes permissibility in an alternative way and iterated admissibility. In each group, the conditions for the latter are stronger than those for the former, which corresponds to the fact that proper rationalizability and iterated admissibility are incomparable but compatible refinements of permissibility within the complete information framework. The essential difference between the two groups is whether a full belief of rationality is needed.

The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency

Chapter 4 Repeated games with complete information

We model sequential, sealed-bid auctions as a sequential game with imperfect and incomplete information. We develop an agent that, through fictitious play, constructs a policy for the auctions that takes advantage of information learned in the early stages of the game, and is flexible with respect to assumptions about the other bidders' valuations. Because the straightforward expansion of the incomplete information game is intractable, we develop more concise representations that take advantage of the sequential auctions' natural structure. We examine the performance of our agent versus agents that play perfectly, agents that also create policies using Monte-Carlo, and agents that play myopically. The technique performs quite well in these empirical studies, though the tractable problem size is still quite small.

We consider the problem of playing a repeated two-player zero-sum game safety: that is, guaranteeing at least the value of the game per period in expectation regardless of the strategy used by the opponent. Playing a stage-game equilibrium strategy at each time step clearly guarantees safety, and prior work has (incorrectly) stated that it is impossible to simultaneously deviate from a stage-game equilibrium (in hope of exploiting a suboptimal opponent) and to guarantee safety. We show that such profitable deviations are indeed possible specifically in games where certain types of “gift” strategies exist, which we define formally. We show that the set of strategies constituting such gifts can be strictly larger than the set of iteratively weakly-dominated strategies; this disproves another recent assertion which states that all noniteratively weakly dominated strategies are best responses to each equilibrium strategy of the other player. We present a full characterization of safe strategies, and develop efficient algorithms for exploiting suboptimal opponents while guaranteeing safety. We also provide analogous results for extensive-form games of perfect and imperfect information, and present safe exploitation algorithms and full characterizations of safe strategies for those settings as well. We present experimental results in Kuhn poker, a canonical test problem for game-theoretic algorithms. Our experiments show that (1) aggressive safe exploitation strategies significantly outperform adjusting the exploitation within stage-game equilibrium strategies only and (2) all the safe exploitation strategies significantly outperform a (nonsafe) best response strategy against strong dynamic opponents.

The author discusses games of both perfect and imperfect information at two levels of structural detail: players’ local actions, and their global powers for determining outcomes of the game. Matching logical languages are proposed for both. In particular, at the ‘action level’, imperfect information games naturally model a combined ‘dynamic‐epistemic language’– and correspondences are found between special axioms in this language and particular modes of playing games with their information dynamics. At the ‘outcome level’, the paper presents suitable notions of game equivalence, and some simple representation results.

An important approach to game theory is to examine the consequences of beliefs that agents may have about each other. This paper investigates respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B's preference if A assigns probability 1 to the choice of a given that B chooses a or b. Respect for public preferences requires that if it is common belief that B prefers a to b, then it is common belief that all other agents respect that preference. Along the lines of Blume, Brandenburger and Dekel [3] and Asheim [1], I treat respect for public preferences as a constraint on lexicographic probability systems. The main result is that given respect for public preferences and perfect recall, players choose in accordance with Iterated Backward Inference. Iterated Backward Inference is a procedure that generalizes standard backward induction reasoning for games of both perfect and imperfect information. From Asheim's characterization of proper rationalizability [1] it follows that properly rationalizable strategies are consistent with respect for public preferences; hence strategies eliminated by Iterated Backward Inference are not properly rationalizable.