analysis of conflict between superpowers through game theory (chicken game)

1. THE ATOMIC CHICKEN
MAX GALARZA HERNÁNDEZ, MSc
max.galarza@pucp.pe
SUMMARY
Game theory does not have the sense in which most people are accustomed to using in
their daily life; it is not related to table, chance or video games, merely recreational activities
as the term game might wrongly suggest. Myerson (2013) defined game theory as “the study of
mathematical models of conflict and cooperation between intelligent rational decision-makers” (p.
1). It is a way of thinking about the strategic interactions between people (players) with
specific interests, for this reason it is very important in economics, computer, political,
psychology, military strategy, logistics and other social sciences. What unifies all these
disciplines of knowledge is a constant concern to think about how participants interested in
themselves behave in strategic interactions and how these interactions should be structured in
order to make better decisions.
During the Industrial and Organizations doctorate syllabus offered by CENTRUM
Católica lectured by Luis Felipe Zegarra, PhD in October 2015 arose the concern that despite
constant threats of confrontation during the Cold War the two great superpowers The United
States of America (US) and The Union of Soviet Socialist Republics (USSR) never attacked
each other. Could it be explained through game theory?
Keywords: Game theory, chicken game, cold war strategy, nuclear conflict, brinkmanship
1. INTRODUCTION
The Cuban missile crisis exemplified the complex and troubling situation that developed
in early October 1962. The Soviet Union placed medium-range ballistic missiles 90 miles
(140 kilometers) from the US territory, possibly as a direct response to Installation of the
American Jupiter missiles stationed in Turkey, bordering country of the USSR in that time.
After intense negotiations, the Soviets ended up withdrawing the missiles of Cuba and
decided to create a massive development program of nuclear weapons. In return, the United
States dismantled its launch sites in Turkey, although this was done in secret and was not
publicly disclosed for more than two decades after the event. The Soviet premier Nikita
Khrushchev did not even reveal this part of the agreement when he was attacked by his
opponents of the Politburo for the mismanagement of the Cuban crisis (Chang & Kornbluh,
1992).
Communication delays during the crisis led to the creation of the Moscow-Washington hot
line to allow reliable and direct communications between the two nuclear powers. During the
Cold War, the superpowers adopted various strategies to deal with the nuclear threat that each
side had set, so policy makers and analysts tried to understand the nature of the strategy in the
early nuclear era. It was adopted the concept of Brinkmanship term coined by US Secretary
of State John Foster Dulles (1956) which consisted of using tactics of fear and intimidation as
strategy to get the opposing faction back. Each party pushed towards dangerous situations on
the brink of war with the intention of having the other side give up positions on international
politics and foreign policy in order to obtain concessions and advantages. However, during

2. the Cold War, neither superpowers faced a direct clash with potentially devastating
consequences
Due to the escalation of nuclear war threat and massive reprisal, both sides were forced to
respond more forcefully. The principle of this tactic was that each faction would prefer not to
yield to the other; However, in practice, one simply has to give way since if neither party
yields, the result would be the worst possible for both. The problem, however, was that
yielding would result in being labeled as the weaker of the two (chicken) and during the Cold
War, both The USSR and The US had a reputation to hold out against their nations, neighbor
countries and allies, which increased the risky bets every time. Since no country gave its arm
to twist, the only way to avoid Mutual Destruction Agreed (MAD) was commitment. British
philosopher Bertrand Russell (1956) compared this situation to the game known as "The
Chicken" and economist Thomas Schelling (1960) was one of the pioneers in theorizing this
subject in his book The Strategy of Conflict.
To understand the situation, many questions were asked. Is the "nuclear deterrent" policy a
credible option? Is Mutual Assured Destruction (MAD) a rational strategy? More
importantly: Is it possible through a rational model based on incentives to demonstrate that
we can live in a world of nuclear weapons without having to witness the catastrophic use of
such weapons?
2. THEORETICAL BACKGROUND
Mathematicians and social scientists, particularly economists, have tried to analyze the
myriad of Cold War nuclear strategies with the use of a mathematical concept of game
theory. This relationship of nuclear tension between superpowers, can be explained through
game theory? An approach was described by Michael Nicholson (1992) in Chapter 4 "The
Chicken Game" (p.75). To understand the game, imagine a contest where two cars are driving
directly against each other (The American film Footloose helps to visualize the example). If
one of the players deviates first of the way to avoid the collision is marked as 'Chicken' and
loses. The car that remains in progress wins and collects the highest possible profitability
(3). In this example, the 'Chicken' will receive a payment of 1 as he and/or she gains some
usefulness in saving the own life. If both "cooperate" and avoid the shock at the same time
each receives a return equal to 2. If both remain in the course (understandable by the desire to
win the contest since they have the incentives to do so) each agent receives a payment of 0.
They are dead or seriously injured after the frontal crash.
When one observes the scenario of the Chicken Game, one tends to emphasize in the pure
strategies of the Nash equilibrium, the basic idea behind this concept is that rational players should
not want to change their strategies if they knew what each of them had chosen to do where it is
verified that the optimal rational situation that the players can reach is when a player finishes
by not cooperating and launching a nuclear attack while the other player is cooperating and
does not reprisal attack or choose less drastic measures to deal with the situation as
diplomacy. Most analysts ie Rasmussen (1989), Binmore (1990), Kreps (1990), Myerson (1991)
agree to apply game theory to almost any social interaction where individuals have some
understanding of how the outcome for one is affected not only by his or her own actions but also by
the actions of others from crossing the road in traffic to decisions to disarm, providing a reasonable
picture of what the opponents' ultimate goals are. Rasmussen(1989) and Myerson (1991)
synthesized that pure Nash equilibrium strategies as a solution concept in which all players

3. execute an action knowing the strategy that maximizes their gains given the strategies of the
other players so that they lack of incentives to make an individual strategy change, however,
this cannot accurately model the real rational results due to each player may guess the others
choice and act consequently. This proposition is not rational either since it derives from the
hypothesis that other players are as instrumentally rationales, they have common knowledge
of this rationality and are well informed of the rules of the game as self, but what if they are
not?
Policy makers might add that the results of the game - while presenting a reasonable
picture of what might be best for opposing sides - is not very useful in trying to apply rational
criteria for the problem of preventing a nuclear nightmare (neither side would benefit from a
shattered planet). Game theorists have established that there would be at least one threat (not
cooperating / not cooperating) or if there is cooperation on both sides, to arrive at some kind
of compromise between total war and stable peace, this is a "Cold War”. These models raise
other questions. Are the threats of nuclear attack credible over time? Can even a more
sophisticated model give an accurate idea of reality? Or in the contrary, a simpler one may
help both theorists and practitioners gain a useful insight into the situation?
"Chicken Game"
(Player 1 = US, Player 2 = USSR Not cooperate(attack) Cooperate (not attack)
Not cooperate (attack) 0, 0 1.3
Cooperate (not attack) 3.1 2, 2
Note: Michael Nicholson (1992) amended by the author.
The following is an explanation of the difficulties posed by the modeling of nuclear
confrontation through game theory. The model may offer a solution that is empirically
reasonable and easy to understand and based on the following assumptions:
Player 1 (US) does not know the decision that player 2 (USSR)
Both players decide their strategies simultaneously.
There are 2 types of strategies: pure strategies and mixed strategies. Pure strategies are the
actions that players can take. Mixed strategies are the distribution of probabilities on such
actions.
The Strategy Profile is the combination of strategies, one per player.
Payments: what the player receives as a result of the strategies played and graphed in the
payment matrix.
Player 1 (US) has 2 pure strategies Do not cooperate (attack) / Cooperate ( not attack)
Player 2 (USSR) has 2 pure strategies Do not cooperate (attack) / Cooperate (not attack)

4. Each cell represents a profile of pure strategies, containing two values: the first value is
the payment to player 1; the second value is the payment to player 2. In this game there are
four profiles of pure strategies. First pure strategy profile, player 1 (US) chooses not to
cooperate and player 2 chooses not cooperate (attack) the payments will be 0 for player 1 and
0 for player 2 (both players die). Second pure strategy profile: player 1 (US) decides not to
cooperate (attack) and player 2 (USSR) decides to cooperate (not to attack). Payments will be
1 for player 1 (receives minor damage) and 3 for player 2 receives more damage).Third pure
strategy profile: player 2 (USSR) decides not to cooperate (attack) and player 1 (US) decides
to cooperate (not to attack) payments will be 3 for player 1 (receive more damage) and 1 for
player 2 (not hurt). Fourth profile of pure strategies: Player 1 (US) decides to cooperate (not
to attack) and player 2 (USSR) decides to cooperate (not to attack) the payment for both
players is 2 (tie, both players are unharmed). Note that in this case Player 1 (US) has a strictly
dominant strategy: Cooperate (not attack): Not attack always gives a higher payout than Not
Cooperate (Attack) given what player 2 does (USSR) Similarly, player 2 (USSR) has a
strictly dominant strategy: Cooperate (not attack) independent of what Player 1 does (US)
When a mixing probability is calculated to be greater than one or less than zero, the
implication is either that the modeller has made an arithmetic mistake or, as in this case, that
he is wrong in thinking that the game has a mixed- strategy equilibrium, in fact, the only
equilibrium is in pure strategies (Cooperate/Cooperate), though, the chicken game has
become a prisoner’s dilemma.
It was established that the best possible scenario for both players was Cooperate /
Cooperate, here last there is a Nash equilibrium because none of the players are willing to
change strategy. The expected result is that there is no aggression between the two
superpowers unless there is a great incentive for the non-aggression pact not to thrive. It can
be ensured that the worst of the expected values of alternation of pure strategies as well as the
benefits of the cooperative solution must outweigh the benefits to the non-cooperative
solution (initiating a nuclear war) these results suggest a possible solution to the dilemmas
which poses a theoretical model of the game of nuclear conflict; but will rational entities
cooperate when faced with a scenario like this? Just consider recent situation of nuclear
threats between North Korea and The United States. Would that be the case? Consider that in
game theory, a player is rational if he maximizes his pay, given what other player does; but,
would Donald Trump and Kim Jung-un act rationally? The situation turns intolerable trying
to guess how the other may act while each player knows the other is doing the same.
Since expected payments for alternations for pure strategies over time are the same as
payments for a sustained cooperative solution, both parties should be more efficient and
avoid the "eye for an eye" of nuclear confrontation if go directly to mutual cooperation.
Another advantage of playing the total cooperation solution is that neither side will run the
risk of playing 'non-cooperative' when the other side plays 'non-cooperative' (which is
possible to play in mixed strategies over time). That possibility would be catastrophic for
both players.
3. CONCLUSIONS

5. Empirically speaking during the cold war between the USSR and the US; there was no
exchange of nuclear attacks between the two parties. There were stances and threats but these
events did not result in a nuclear confrontation, the ability to retaliate was more useful than
the ability to withstand an attack and the threat of uncertain reprisal was more effective than a
precise threat.
The idea of adding "threats" to this model would be useful for future investigations,
particularly in the latest North Korea and US escalate where their leaders consider themselves
as rational agents and treat the other as a causal deterministic being. Game theory is a useful
way of characterizing a problem, but in terms of predicting if someone would press or not the
button, it shall correspond to causal theory to explain.
The Nash Equilibrium is always the optimum in these circumstances, which is why it is so
important. The question is how to get there.
References:
Binmore, K. (1990) Essays on the Foundations of Game Theory. Oxford: Basil Blackwell.
Brinkmanship (2015): Foreign policy. Written by the editors of the Encyclopedia
Britannica. Http://www.britannica.com/topic/brinkmanship
Chang, Laurence & Peter Kornbluh, eds. 1992. Cuban Missile Crisis, 1962: A National
Security Archive Documnlents Reader. New York: New Press
Kreps, D. (1990) Game Theory and economic modeling. New York: Oxford University Press.
Myerson, R. (1991) Game theory: Analysis of conflict. Cambridge, MA: Cambridge
University Press.
Nicholson, M. (1992): Rationality and the Analysis of International Conflict. ISBN
052139810X,
9780521398107https://books.google.com.ec/books/about/Rationality_and_the_Analysis_of_I
nternat.html?id=y9w4TF_GItoC&redir_esc=y
Rasmussen, E. (1989) Games and Information. Oxford: Blackwell.
Russell, Bertrand W. (1959) Common Sense and Nuclear Warfare London: George Allen &
Unwin, p30: Psychology Press, 1959 ISBN 0415249945, 9780415249942
Schelling, T. (1960): The Strategy of Conflict, Harvard University Press , ISBN 0-674-84031-
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