Strategic games, with a fare-setting example

Meaning of a strategic game. A strategic game is a situation of interdependence: when a decision maker chooses among the actions open to her, she also considers how the others will respond, because her benefit depends on their choices as well as her own, and her choice affects theirs. This is unlike the textbook case of perfect competition, where a firm is assumed to ignore its rivals; in an oligopoly, with a few large firms, each firm has to allow for its competitors' reactions. Game theory is the study of such interactions.

What a strategic game is made of. The participants who choose a course of action are the players; each player's plan of action is a strategy; and the gain or loss that each player receives once the strategies have been played is the payoff. Players are assumed to be rational, each choosing so as to maximise her own payoff and expecting the rivals to do likewise. An outcome is an equilibrium when, given what the others are doing, no player has a reason to change her choice.

Example (our own): two airlines setting fares. Two airlines fly the Delhi–Mumbai route. Each must decide, without knowing the other's decision, whether to charge a high or a low fare for the coming month. Monthly profits in ₹ crore are shown as (Airline A, Airline B):

Why it is strategic. A's profit from any fare depends on B's fare: a high fare earns A ₹50 crore if B also charges high, but only ₹20 crore if B undercuts it.

A's best reply. If B charges high, A earns 60 by going low against 50 by staying high. If B charges low, A earns 30 by going low against 20 by staying high. Whatever B does, the low fare pays A more, so it is A's dominant strategy, the choice that is best regardless of the other player's move.

B's best reply. The table is symmetric, so the same reasoning makes the low fare B's dominant strategy as well.

The outcome. Both charge low fares and earn ₹30 crore each. At (low, low) neither airline gains by switching alone (switching to high would cut its profit from 30 to 20), so it is the equilibrium. Yet both would earn ₹50 crore if both kept fares high. Each player's pursuit of its own interest leads to a result worse for both than cooperation would give, which is the structure of the prisoners' dilemma. It also shows why, even if the two agree to keep fares high, each has a reason to cheat on the agreement for its own gain.

Conclusion. A strategic game is a decision problem in which each player's payoff depends on the choices of all, so each must predict the others' moves. In the fare example each airline reasons about the other, both end up with low fares, and the outcome is stable but leaves both worse off than they could be together.