The Doklam standoff between India and China continues to attract daily press coverage although the rhetoric of escalation & war has been reduced significantly in past few days.
We take a game theory approach to evaluating this standoff that has been debated from strategic, political and economic angles.
While a few commentators have published on game theory aspects of the dispute but approach has been fairly basic using Prisoners dilemma game to evaluate the strategic options available to both countries. The standoff can be better modelled as a game of hawk-dove where there is no particular equilibrium and assumption is that cost of war is higher than the reward associated with the win.
Prisoner's dilemma game
The simplest, prisoner's dilemma game can be modelled by assuming that both the countries have two strategies - Stay or Attack. Payoffs in the game are structured in a way that the Stay option for both countries yields the highest payoff while if both countries Attack the resulting payoff is the lowest. In case China Attacks and India Stays (or Retreats) the pay off for China is higher and vice versa in case India Attacks and China adopts Stay strategy. The matrix of payoffs is provided below (numbers are purely used to denote an ordinal ranking of strategies ):
|INDIA||Stay||4, 4||0, 5|
|Attack||5, 0||0, 0|
While the game has two strategies but as the Attack strategy is the dominant strategy the game has a sub-optimal Nash equilibrium (Attack, Attack with 0,0 as payoffs). Adopting an attack strategy will always give higher or equal payoffs to a player in the above game (irrespective of what other player is doing) and as both players adopt the Attack strategy the resulting Nash equilibrium is sub-optimal.
Ideally, if both players cooperate then a Stay, Stay option with higher payoffs (4, 4) is Pareto optimal. A prisoner's dilemma game is structured in a way that the reward from a victory is higher than the cost of a war. As a result Attack strategy becomes the preferred strategy. However, we believe that cost of war is higher in this case than the gains of victory.
A Hawk-Dove game used more in evolutionary biology is a better reflection of the current standoff at Doklam.
In this game, the payoffs are structured in a way that the cost of attack (or war) is always more than the value of the payoff. Evaluating the payoffs from an India-China perspective we find that controlling a rump of land high up in Himalayas might yield some national pride for both countries and also send signal of their strength to other countries in the region but the costs will include another few decades of hostility & distrust and certain amount of trade and investment embargoes that will result in event of a war. The costs, therefore, are higher than the reward.
The game is structured as follows:
|Strategy||Attack (Hawk)||Stay (Dove)|
|INDIA||Attack (Hawk)||-2, -2||4, 0|
|Stay (Dove)||0, 4||2, 2|
Unlike the prisoner's dilemma, the above game has no dominant strategy and hence no dominant strategy equilibrium.
There two possible nash equilibria are (Attack, Stay and Stay, Attack) where the first player does opposite of what he expects the other player will do. So if India expects China to attack with certainty then it should simply retreat and the same applies to China.
Only when both players are convinced that other will remain a Hawk will the game collapse to Stay, Stay strategy option! India and China are trying to convey the very same message to each other and also to the world. China by maintaining that India has entered into its territory while India maintains that this particular piece of tri-junction involving India-Bhutan-China is a disputed territory & also critical to its national security. The actual game is structured as follows:
|Attack (Hawk)||Stay (Dove)|
|INDIA||Attack (Hawk)||(V/2 - C), (V/2 - C)||V, 0|
|Stay (Dove)||0, V||V/2, V/2|
Here V is the value of the payoff while C is the cost of war. C>V (cost of war higher than the value of payoff) is the critical assumption and therefore V/2-C has a negative value. The probability of either player playing the hawk option, therefore, becomes V/2C and of playing dove is the complement of it (1-V/2C).
Another form of the above is called a game of chicken where each driver in a car is racing towards the other and each has to decide whether to go straight ahead or swerve at the last moment. Again each player will adopt a strategy opposite of what the other player is doing. For e.g. if India is certain that China will attack it would pay to swerve away while if China is certain that India is going straight and crashing it will swerve away.
One way out is for any of the players to pull off its steering wheel thereby convincing the other that it has no choice left in which case the other player will swerve away.
Currently, both the countries are trying to convince the other that it has pulled out its steering wheel. When both players are convinced that the other player will not chicken-out the game will result in a Stay, Stay outcome.
As the time elapses, the Doklam standoff is appearing like a protracted standoff that will take a while to resolve. If history is any indicator then once can recall the Sumdorong Chu standoff between India & China that occurred in 1986 where troops were amassed by both countries and war noises were made by China but eventually after close to a year a breakthrough was achieved and troop levels were very slowly scaled down.
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