Information, decision-making and deception in games Dongxu Li a, ⁎, Jose B. Cruz Jr. b a General Motors Corporation, R&D, Warren, Michigan 48090, USA b Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA abstract article info Article history: Received 12 January 2008 Received in revised form 20 April 2009 Accepted 10 May 2009 Available online 15 May 2009 Keywords: Decision-making Zero-sum game Deception Nash equilibrium Mixed strategy Modeling deception in a real-world conflict situation is usually difficult. For a better understanding, we study deception through a fundamental relationship between information and decision-making. Under a probabilistic framework, we consider a zero-sum game with an asymmetrical structure, where player 1 receives additional information and player 2 has the potential to inject deception. We derive accuracy conditions on the information obtained by player 1, which can lead to a better decision. The feasibility of deception is further explored, which is conditioned on the quality of deceptive signals generated by player 2. We classify deception into passive and active deception. © 2009 Elsevier B.V. All rights reserved. 1. Introduction Information plays an important role in decision-making problems, and the study of their relationship has a wide spectrum covering artificial intelligence, economics, business, statistics and control [6,10,11]. A decision-making problem is usually formulated as an optimization problem with a utility function representing potential payoffs/costs. However, relevant information available to a decision- maker is often imperfect [13], such that probabilistic models are often adopted. Thus, the statistical characteristics of the information are crucial, which determine the relevance of the problem model created by the decision-maker and in turn its potential payoffs. Intuitively, more (relevant) information is helpful in reducing uncertainty, thus leading to a better payoff. Information value is usually defined through the difference in the payoff induced by the extra information [6,11]. For years, this idea has been explored in various fields. In [2], a stochastic control problem was studied, where it has been shown that inclusion of potential information (measurement) in the future is helpful in reducing the uncertainty involved in decision-making at the present time, and thus a better performance can be attained. A similar idea has also been discussed in a team setting with more than one decision- maker [10]. In [16], value of information to a risk-averse decision- maker was studied under the information system framework. Information has also been studied in the context of game theory [3]. It is well known that game theory provides a rigorous tool to analyze interactions among multiple decision-makers, each with its own optimization objective. In recent years, game theory has become increasingly important in politics, social sciences, military and engineering applications, because it can better capture the conflict nature in a situation involving multiple players. Compared to normal decision analysis, game analysis can not only offer a decision suggestion to a decision-maker but also provide a valuable prediction on its opponents' counteraction. With the recent development in the technologies of autonomous vehicles and command and control systems, game theory has become an indispensable tool in modeling and analyzing dynamic situations in modern military operations [5,13,20]. These systems rely on a large amount of intelligence infor- mation to be processed, and apparently, the information fed into the systems has a substantial impact on the system performance. The dependence of decision-making on information implies another interesting direction of research — deception. This is especially important in a game situation, where players may try all means to degrade their opponents' decisions to increase their own returns. In this sense, deception appears to be a useful strategy in hand for game players. The theme of deception is to manipulate the decisions of a decision-maker by changing its base information in favor of a deceiver. Generally speaking, the purpose of deception is to conceal reality by inserting “noise”, or to mislead the decision-maker with biased information. Although deception has received a lot of attention, to date, the literature on deception is still relatively sparse. In [7], the effect of deception on decision-making was investigated, and it has been shown that decisions of a decision-maker can be adjusted by changing its belief of the state of nature. This idea was further extended to a bargaining situation between a seller and a buyer in [8]. In [4], a deception game problem was formulated and the existence of a value function was proved. The effect of deception has also been studied through a stochastic pursuit-evasion game where the Decision Support Systems 47 (2009) 518–527 ⁎ Corresponding author. E-mail address: li.447@osu.edu (D. Li). 0167-9236/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.dss.2009.05.001 Contents lists available at ScienceDirect Decision Support Systems journal homepage: www.elsevier.com/locate/dss