Game Theory: Nash Equilibrium and Strategic Thinking

What is a game in the formal sense

Game theory is a mathematical analysis of strategic interactions, where outcomes depend on the choices of multiple agents. A “game” here is a formal model including: players, their possible strategies, a payoff function (what each receives for every combination of strategies).

John von Neumann and Oskar Morgenstern (“Theory of Games and Economic Behavior”, 1944) laid the foundations. Their main result is the theorem on zero-sum games: in a two-player zero-sum game (one's gain = other's loss) there always exists an optimal mixed strategy.

John Nash (“Beautiful Mind”) generalized the result to non-zero-sum games. Nash equilibrium: a situation where no player wants to unilaterally change their strategy, knowing the strategies of the others. This is not necessarily the best outcome—it is a stable outcome.

Prisoner's dilemma

The most famous example in game theory. Two prisoners, jointly arrested, are interrogated separately. Each can cooperate (remain silent) or betray (testify against the other). Payoff matrix: both silent—1 year of prison for each. Both betray—3 years for each. One betrays, the other is silent—betrayer goes free, silent one gets 5 years.

The dominant strategy for each is to betray (regardless of what the other does). Nash equilibrium—both betray. Yet this is worse for both than if both remained silent. This demonstrates a fundamental contradiction between individual rationality and collective welfare.

Prisoner’s dilemma in reality: arms race, price wars, environmental pollution, recycling, overtime work. Why do people cooperate anyway? Repeated games (the “tit-for-tat” strategy), reputation, norms, regulation.

Question for reflection: Find a prisoner’s dilemma in your organization or industry—a situation where individual rationality leads to a collectively worse outcome. What mechanisms can lead out of it?