Game theoretic solution to Doklam

The only mutually beneficial course of action in Doklam is for India and China to pull their troops

It has been two months and both sides have refused to budge. The Chinese insist on a unilateral Indian troop withdrawal while the Indians want a mutual troop withdrawal.  As the war clouds over Doklam refuse to recede, let us try and understand the standoff from the point of view of Game Theory.
 

Game theory is a branch of mathematics that analyses how decisions are made in conflict situations.  The decision makers are the “players” in a “game”. Each player chooses from a set of strategies available to him. The choice of strategies by the players results in an outcome.  Each outcome is associated with a payoff (expected utility) for the player.  Players are assumed to be rational in that they would prefer a higher payoff to a lower one. And each player assumes that other players are rational in the same sense.
 
To construct a game theory model of the Doklam standoff, let us assume that the two players, China and India, have to choose between three strategies: Withdraw, stay or escalate. The “stay” strategy means to maintain current troop levels and the “escalate” strategy means to increase troop levels. There is a cost to each player if he chooses to Stay and a higher cost of mobilising troops if he chooses to escalate. Since escalation is only limited to increasing troop levels it does not automatically result in war. 
 
Each player can then be reasonably assumed to have the following order of preferences for the outcomes:

 
Withdraw when the other stays (total defeat), withdraw when the other escalates (defeat), stay when the other escalates (partial defeat), both escalate, both stay, both withdraw, escalate when the other stays (partial victory), escalate when the other player withdraws (victory), and stay when the other withdraws (total victory).
 
We can assign payoffs 0, 1, 2, 3, 4, 5, 6, 7, 8 for the above outcomes respectively, where the numerical values of the payoffs have no meaning except to represent the ranking of the preference.
 
We construct a payoff matrix whose rows represent the choices for India (row player) and the columns the choices for China (column player). The nine cells of the matrix then represent the nine possible outcomes. The payoffs are written in each cell as an ordered pair of numbers. The first number in the pair is the payoff for India and the second number is the payoff for China (Fig 1).
 
It is clear from the payoff matrix that a player is always better off choosing to stay rather than withdraw, irrespective of the other player’s choice, i.e. the strategy to stay dominates the strategy to withdraw.  Hence we can remove the strategy to withdraw from both players’ choice of strategies.
 
This reduces the game to the following payoff matrix (Fig 2):
 
This is the classic game of prisoner’s dilemma. The dominant strategy in this game is to escalate. This leads to the only equilibrium in the game, which is (escalate, escalate).  Note that the both India and China are better off if they end up at the (withdraw, withdraw) outcome, which is the Pareto Optimal outcome. The only way this outcome is possible if both sides decide to cooperate.
 
Will the (escalate, escalate) outcome lead to war? Consider the situation where the two players do not cooperate. This leads to the outcome where both sides have mobilised troops and are at a standoff. The standard game used to describe a conflict situation in which two players appear to be heading for a clash is the game of chicken.
 
In this game, two drivers race their cars towards each other.  Each player has the choice of swerving or not swerving. The player who “chickens out” and swerves first gets a lower payoff than the player who holds his nerve and does not swerve. If neither player swerves then the cars collide and result in the lowest payoff for both players. After escalation, Indian and Chinese soldiers standing eyeball to eyeball, waiting for the other to blink, can be modelled as a game of chicken.
 
The choices of strategy are to stay or attack (Fig 3). The stay strategy means to stay in the escalated position of the last game. Each player has the following order of preferences for the four possible outcomes:
 
Both players attack (War); one stays and the other attacks (Defeat); both stay; one attacks and the other stays (Victory).
 
We can assign payoffs of 0, 1, 2 and 3 respectively for the four outcomes. Again, the numerical values of the payoffs have no meaning except to represent the ranking of the preference.
 
As in the last game we construct a payoff matrix whose cells represent the four outcomes.
 
So what is the likely outcome of the standoff according to this model? It can be easily verified that there is no dominant strategy in this game. Hence there is no dominant strategy equilibrium.  Consider the situation from the viewpoint of any one particular player. If this player is convinced the other player is going to stay, then he is likely to attack rather than stay.  So the (stay, stay) outcome is not a stable outcome.
 
Similarly, if the player is convinced that the other side going to attack, then he would prefer to stay rather than risk a war. So the (attack, attack) outcome is also unstable.  Since both players want to do the opposite of what the other player is doing, the only stable outcomes are where one player withdraws and the other escalates. These two outcomes, which are underlined in the matrix, are the only equilibria in this game. These equilibria are called the Nash equilibria, after the mathematician John Nash.
 
In an actual game of chicken, if one player rips out his steering wheel in view of the other driver it visibly forecloses his choice to swerve. And hence the other player is forced to swerve. China is trying to convince India and the rest of the world that that they do not have the option to swerve. Their position is that India has transgressed on their national sovereignty and they will have no choice but to resort to an attack.
 
Many analysts, convinced by the Chinese rhetoric, assume that the Chinese will ultimately resort to an attack. Hence, India will be better off withdrawing immediately.
 
India on the other hand has called for a mutual withdrawal. To achieve this it needs to convince China that it has ripped out its steering wheel and will not swerve. When both players are convinced that the other will attack, the game will collapse to the (stay, stay) outcome.  This means that the conflict ends at the original prisoner’s dilemma game.
 
Then the two countries must cooperate to reach the mutually beneficial outcome of mutual withdrawal instead of needlessly expending resources in a futile standoff. 

The writer is an economics and financial consultant