International Trade

Games with Dominant Strategy Equilibrium

Example - Cartel

There are two firms in the market, and they can choose to operate independently (strategy I) or form a cartel (strategy C). The payoffs are as follows:

  • If they form a cartel, they agree to limit production, hence increasing price, so they both gain 8. [1]
  • If they both operate independently, they both gain 4. [2]
  • If they agree to form a cartel, thus increasing the price, but one firm betrays the other by producing more than agreed, then that firm gains a lot while the other loses a lot. [3]


  • How should the two firms operate to maximise their gains? Consider Firm 1:

  • If Firm 2 chooses C, [4] then Firm 1 has a higher payoff with I. [5]
  • If Firm 2 chooses I, [6] then Firm 1 has a higher payoff with I. [7]


  • Thus, I is a dominant strategy for Firm 1, because it gives the higher payoff regardless of the other player's strategy.

    The same reasoning applies for Firm 2:

  • If Firm 1 chooses C, [8] then Firm 2 has a higher payoff with I. [9]
  • If Firm 1 chooses I, [10] then Firm 2 has a higher payoff with I. [11]


  • So I is a dominant strategy for Firm 2 as well. This leads to a dominant strategy equilibrium at (4, 4). [12]
    If a certain strategy pays a player the highest payoff, regardless of the other player's strategies, then that strategy is known as a dominant strategy.

    If both players have dominant strategies, the point which they both choose is known as the dominant strategy equilibrium.

    Analysis

    We see from our example that the (C, C) strategy [1] is Pareto Superior to (I, I). [2] However, unless the players co-operate in choosing their strategies, they will choose the inferior (I, I). The dominant strategy equilibrium does not always provide the best result.

    If the players choose (C, C), either player can gain by moving to I unilaterally. In other words, if they agree to form a cartel, either player can gain by reneging on the agreement. This is why cartels are considered unstable and easy to collapse. Both players try to maximise their own profit by defecting. However, as a result, both of them experience reduction of profit. Therefore, it is known as a "tragedy of commons".

    How do firms keep a cartel strong?

  • Invoke severe punishments for firms that renege on the agreement.
  • If the game is played repeatedly, a player that reneges is not likely to be trusted, so will not be able to form a cartel with others again.
  • [Next] Games with Dominant Strategy Equilibrium
    [Topic] Application of Game Theory to International Trade


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