Advisor: Yeong-Sung Lin Presented by I-Ju Shih 2011/9/13 Modeling secrecy and deception in a multiple- period attacker–defender signaling game 1.

Advisor: Yeong-Sung Lin Presented by I-Ju Shih 2011/9/13 Modeling secrecy and deception in a multiple- period attackerdefender signaling game 1

Agenda 2011/9/13 Introduction Signaling game Model formulation for repeated game Attacker observes defensive investment from the previous period Attacker does not observe defensive investment Conclusions and future research 2

Introduction 2011/9/13 Most applications of game theory to homeland-security resource allocation so far have involved only one-period games. Dresher (1961) was among the first researchers to apply game theory to military strategic interactions. However, he did not explicitly model deception and secrecy. Recent game-theoretic research has also indicated that publicizing defensive information instead of keeping it secret may help to deter attacks. 4

Introduction 2011/9/13 In practice, however, security-related information such as defensive resource allocations is often kept secret. There is a long tradition of deception in the military arena, as well as in business and capital ventures. Few of these studies have focused specifically on disclosure of resource allocations. Defenders might also have incentives to deceive by either overstating or understating their defenses, to deter or disinterest potential attackers, respectively. 5

Introduction 2011/9/13 Zhuang and Bier (2007) indicate that truthful disclosure should always be preferred to secrecy, which is not surprising, since their model is a game of complete information. Attacker uncertainty about defender private information can create opportunities for either defender secrecy or deception. Zhuang and Bier (2011) found that defender secrecy and/or deception could be strictly preferred in a one-period game in which the defender has private information (i.e., the attacker is uncertain about the defender type). 6

Introduction 2011/9/13 Secrecy has been sometimes modeled as simultaneous play in game theory, since in a simultaneous game, each player moves without knowing the moves chosen by the other players. Some researchers have modeled deception as sending noisy or imperfect signals to mislead ones opponents. Hespanha et al. (2000) and Brown et al. (2005) defined deception in a zero-sum attacker-defender game as occurring when the defender discloses only a subset of the defenses, in an attempt to route attacks to heavily-defended locations. 7

Introduction 2011/9/13 By contrast, this paper defines deception as disclosing a signal (in the domain of the action space) that differs from the chosen (hidden) action. This paper applies game theory to model strategies of secrecy and deception in a multiple-period attacker-defender resource-allocation and signaling game with incomplete information. 8

Introduction 2011/9/13 Games are classified into two major classes: cooperative games and non-cooperative games. In traditional non-cooperative games it is assumed that 1. The players are rational. 2. There are no enforceable agreements between players. 3. The players know all the data of the game. However, real-game situations may involve other types of uncertainty. 9

Introduction 2011/9/13 In this paper they focus on the case where the defender does have private information, while the attacker does not. In this case, they allow two types of updates about the defender type the attacker updates his knowledge about the defender type after observing the defenders signals, and also after observing the result of a contest (if one occurs in any given time period). 10

Signaling game 2011/9/13 12 Games are classified into four major classes.

Signaling game 2011/9/13 13 A signaling game is a dynamic game of incomplete information involving two players, a Sender and a Receiver. It involves two players one with private information, the other without and two moves: first the informed player (Sender, she) makes a decision, she "sends a signal". then the uninformed player (Receiver, he) having observed the informed players decision but not her private information makes a decision, he "reacts to the signal".

Signaling game 2011/9/13 14 The timing of the game is as follows: Nature selects a type t i for Sender from a set of feasible types T = {t 1,..., t I } according to a commonly-known probability distribution p(.), where p(t i ) > 0 (prior belief) for every i {1,...,I} and p(t i ) = 1. Sender observes t i and, on the basis of t i, chooses a message m j from a set of feasible messages M = {m 1,...,m J }. Receiver observes m j and, on the basis of m j, selects an action a k from a set of feasible actions A ={a 1,...,a K }. Payoffs are realised: if nature has drawn type t i, S has chosen message m j and R has selected action a k, then payoffs for S and R are u S (t i, m j, a k ) and u R (t i, m j, a k ).

Advisor: Yeong-Sung Lin Presented by I-Ju Shih 2011/9/13 Modeling secrecy and deception in a multiple- period attacker–defender signaling game 1.

Documents

simultaneous game

repeated game attacker

game model formulation

game of complete information

model deception

applications of game

defensive information

period games