Strategic games, with an airline fare example

Meaning of a strategic game. In many decisions what a person gets depends only on her own choice. A situation is strategic when it does not: each decision maker, while choosing among her actions, has to think about how the others will respond, because their choices affect her benefit and hers affect theirs. A strategic game is any such situation of interdependent decisions, studied by game theory. Firms in an oligopoly are the standard case, since each must allow for its rivals' reactions; but students sharing a flat, voters and political parties face strategic games too.

Its elements.

• Players: the participants who choose a course of action.
• Strategies: each player's plan of action, simple or depending on earlier moves.
• Payoffs: the gain or loss each player receives at the end, which depends on the strategies chosen by all players together.
• Rationality: each player tries to maximise her own payoff and expects her rivals to do the same.
• Common knowledge of the rules: every player knows the number of players, the strategies open to each, the payoffs, and that all are rational.
• Timing: players may move at the same time (a simultaneous game) or one after another (a sequential game), and this changes how they form their strategies.

Example: two airlines on the Delhi–Bengaluru route. Our own figures. Two airlines, A and B, each choose a fare for the coming month, high or low, without knowing the other's choice. Monthly profits in ₹ crore are (A, B):

• A reasons: if B charges high, a low fare gives me 8 instead of 6; if B charges low, a low fare gives me 4 instead of 2. A low fare is A's best choice whatever B does, a dominant strategy. B's payoffs are the mirror image, so B reasons the same way.
• Both charge low fares and earn 4 each. Neither gains by switching alone (switching to high would cut its profit from 4 to 2), so (low, low) is the equilibrium: a strategy pair from which no player wants to deviate.
• Yet both would earn 6 if both kept fares high. Here each airline's best choice happens not to depend on the rival's, because a low fare is dominant; but each airline's payoff depends on the other's fare (A earns 8 or 4 from a low fare according to what B does). That interdependence of payoffs is what makes this a strategic game.

Conclusion. A strategic game is a situation in which players' payoffs depend on one another's choices, so each must anticipate the others' responses. The airline example shows how rational players choosing strategies to maximise their own payoffs can reach an equilibrium that leaves both worse off than cooperation would.