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Alex Ruiz

12/05/2010

EC: 405.01: Game Theory & the Economics of Information

Defense & Peace Economics: An Economic Analysis of Military Intelligence

Shirley J. Ho; Department of Economics, National Chengchi University, Taiwan

Introduction:

A CBS news article, published in June 2010, discusses arrest of 10 Russian, long-term, deep-cover spies living throughout US East Coast:

“FBI: 10 Russian Spies Arrested in U.S”



Addresses the outstanding issue of moral hazard, where spies of foreign countries are free from risk, such that the contracting country cannot observe their actions while undercover.

Aldrich, 1998 cites MI5’s Double Cross System, an anti-espionage operation during WWII, as example of defection, where Nazi agents were captured, used to send disinformation back to Nazi party.

Enemy countries can manipulate flow of information through defection.

Issue of moral hazard presents significant setbacks to contracting & discovery process.

Incorrect military intelligence may lead to false conclusions by rival country & disastrous outcomes.

This paper analyzes, under asymmetric information, motivations of given countries to hire a spy, outcomes which could arise from discovery of evidence in a rival country, and issues presented when a spy is contracted.

Players & Assumptions:

This game involves the strategies of two players, Country B (Player 1) and Country A (Player 2). They possess a prior belief,[pic], that new weapon exists (y), and[pic] that new weapon does not exist (n).

Truth Statement: [pic]; Action Profile: [pic]; Welfare: [pic], where [pic] & [pic]

Two assumptions:

1) [pic]

[pic]

P is a strictly dominated pure strategy when the truth statement is (y), whereas W is strictly dominated pure strategy when truth statement is (n).

2) [pic]: Country A must defend itself.

[pic]: Country A would lose money by attacking unnecessarily.

Model Timing and Strategies:

A simultaneous-move game exists between Countries A and B: it is impossible for Country A to observe the decision of Country B, which must choose between developing and not developing a new weapon. However, Spy 1 must move sequentially after Country A decides whether to hire him, who then decides to exert high or low effort. Finally, Spy 1 then decides whether to report truth regarding the existence of a new weapon, or engage in a contract renegotiation by defection.

Bayesian Nash Equilibrium:

Players only seek to maximize their expected utility/payoff, given the beliefs of other players. In this respect, each player’s belief is a function of the beliefs of all other players. Thus, the best responses of each country are not easily derived.

The welfare difference between knowing and not knowing whether Country B has developed a new weapon is primary motivation for Country A, captured by its welfare equilibrium, to hire a spy.

If[pic], Country A believes that B has developed a new weapon & will choose War (W).

Country A’s Welfare: [pic]

If[pic], Country A believes that B has not developed a new weapon & will choose Peace (P).

Country A’s Welfare: [pic]

We equilibrate above two equations to derive Country A’s equilibrium welfare:

[pic] = [pic]

[pic]

[pic]

[pic]

Note: Equilibrium welfare is expressed strictly in terms of Country A, as the game begins because Country A suspects Country B of developing a new weapon, and strategizes accordingly.

Solutions to Issues of Moral Hazard & Defection:

Contract,[pic] involves report [pic] regarding truth statement, & reward[pic]; Binary Choice: [pic] Probability of discovery:[pic], where [pic] & Effort cost[pic]; Assumed that:[pic] & [pic]

Spy 1 Expected Utility:[pic]

Note: probability of truth discovery increases with effort level ([pic]) & increases cost of effort ([pic])

Country A’s expected welfare depends upon information reported by its contracted spy:

[pic]

[Where [pic] is the probability that the spy will discover the new weapon certainly with effort[pic]. Country A will thus choose W.]

[Where [pic] is the probability of no discovery. Country A will thus choose P.

The Moral Hazard Condition

Exists when[pic], where finding hazard is denoted by[pic], and report is denoted by[pic]. The scenario when a spy’s finding is equal to report, where [pic] for all[pic]. Spy has incentive to shirk due to a low risk of being observed by the contracting Country A.

Moral Hazard Solution: [pic]

A spy’s expected utility from effort must be greater than/equal to expected utility/reward from no effort in discovery.

The Defection Condition

Exists when[pic]. Spy 1 can defect and sell information back to the rival Country B, foregoing reward[pic]. The spy will change report to [pic] if Country B accepts Spy 1’s request according to belief[pic], and pays ransom[pic]. Spy 1 will acquire two rewards: one for negative report ([pic]), and one for changing this report ([pic]).

Defection Solution:[pic]

Reward to Spy 1 ([pic]) must be greater than/equal to expected benefit to Country B (difference between Spy 1 defecting and telling truth) as result of buying back silence of Spy 1:

[pic]

Model Implications:

1) Country A will always choose Peace when no discovery (n); Country B will always choose War when weapons exist (y), and Peace when weapons don’t exist (n).

2) Country A’s equilibrium welfare outcomes based upon beliefs; both smaller than if Country A was certain.

3) Moral hazard eliminated when[pic]. Exerting effort is always a dominated strategy.

4) Probability of no discovery will theoretically increase to 1 as expression, which describes certainty of discovery, approaches a negative value (benefit to Country B of concealing truth is sufficiently high). Cost of hiring Spy 1 should be less than benefit of uncovering a secret that bears the utmost value to Country B. (Country A will not find it worthwhile to initially hire Spy 1).

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