Game Theory and Cold War Nuclear Confrontation, Part I

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    The Game of "Chicken" and Cold War Nuclear Weapon Strategies Revisited: An Informal Game Theoretical Approach by Steve Lee

    During the Cold War, opposing sides adopted various strategies to deal with the nuclear threat that each opposing side possesed. Both policy makers and policy analysts, attempted to understand the nature of strategy in the nuclear age.

    To understand the situation, many questions were asked. Is the policy of 'nuclear deterrence' a credible option? Is Mutually Assured Destruction (MAD) a strategy that is rational? What about détente? Most importantly, is it possible -- through an incentiv e-based rational model -- to show that we can live in a world of nuclear weapons without having to witness the catastrophic use of those weapons?

    Mathematicians and social scientists (in particular, economists) have tried to analyze the myriad of Cold War nuclear strategies with the use of a mathematical concept known as Game Theory (to find out more about Game Theory and its background, click: What is Game Theory or History of Game Theory). In particular, the game theorists have focused in on a game know n as "chicken."

    To understand "Chicken," imagine a contest where two cars are coming straight at each other (see a James Dean movie for an illustrative example). If one of the player turns first to avoid the collision -- he/she is branded a 'chicken.' The one who stays t he course will then collect the highest possible payoff -- which is 3 in this example. The 'chicken' will recieve a payoff of 1 (in this example) -- since he/she gets some utlity from saving his/her own life. If they "cooperate" and avoid each other AT TH E SAME TIME, they will each receive an equal payoff of 2 (in this example). If they both stay the course (which is not ridiculous since they have the incentives to do so), they will each receive a payoff of 0 -- i.e., they will be either dead or gravely i njured.

    The following (Figure 1) is adapted from Microeconomic Theory, 5th ed., by Walter Nicholson. It is a game that has been used to explain Nuclear Deterrence/Mutually Aided Destruction (MAD) scenarios of the Cold War (Nicholson, p.643). The game is in Normal Form. The two Pure-Strategies Nash Equilibria are blinking. The Mixed Strategies Nash Equilibrium is (Cooperate, Not Cooperate)=(1/2, 1/2) for both players 1 (row and first payoff) and 2 (column and second payoff).

    Figure 1. "The Game of Chicken," from Nicholson, 1992, p.643.
    (Player 1 = ROW, Player 2 = COLUMN)CooperateNot Cooperate
    Not Cooperate3,10,0

    (Note: All "Chicken" games do not have these sets of payoffs. However, the conclusions of this piece should still apply with other sets of payoffs where the game being played is "Chicken." Of course, this is due to the informal nature of this work.)

    When most analysts look at the "Chicken" scenario, they tend to emphasize on the pure-strategies Nash Equilibria. They notice that the most rationally optimal situation that the players can attain is to have one player wind up Not Cooperating (in our nucl ear example, it might be to launch a nuclear attack) while the other player is Cooperating (i.e., not launching a retaliatory attack or choosing less drastic measures to deal with the situation (such as diplomacy)). Most analysts will agree that the impli cations from the pure-strategies equilibria provide a reasonable picture of what the ultimate goals of the two opposing sides are. However, some of these analysts correctly hypothesize that the pure-strategies Nash Equilibria may not accurately model the actual outcomes. Policy makers might add that the outcomes of the game -- while presenting a reasonable picture of what the opposing sides' best case scenario might be -- is not very useful in trying to apply rational criteria to the problem of preventing a nuclear nightmare (presumably, neither side would benefit from a shattered planet).

    Some of the alternative 'solutions' to this scenario has involved stretching the limits of what is an acceptable solution beyond the usual Nash Equilibrium/Equilibria criterion. A few theorists have said that there would be at least a threat of (Not Coope rate, Not Cooperate) (if not all out non - cooperation on both sides) to arrive at some sort of compromise between all out war and a stable peace (i.e., a "cold war").

    Others have modified the "Chicken" game model to add a level of sophistication that the original model allegedly lacks. The hope of these theorists and practioners is to have a set of solutions available that would allow for credible alternate strategies to all out war or a unstable conditions between the opposing forces.

    These alternative models raises other questions. Are the threats of nuclear attack credible over time? Can even the most sophisticated model give us an accurate picture of reality? Wouldn't it be more 'efficient' to use a simpler model that can help both theorists and practioners get a useful view of the situation?

    In the next section, another explanation is offered for the difficulties raised by modeling nuclear confrontation through game theory. The following model should offer a solution that is both empirically sound and is fairly simple to understand.

    To go to the next section click: more.

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