Game Theory in Economics and Strategic Management

From Abstraction to Practice

All game theory concepts—Nash equilibrium, SPNE, ESS, mechanism design—were developed as abstract analytical tools. But their true value is revealed in applications: explaining real market behavior and shaping companies’ strategic decisions.

Oligopoly: Two Canonical Approaches

Cournot Model (competition by output): Firms simultaneously choose production volumes $q_1$, $q_2$. Equilibrium: $q^* = \frac{a-c}{3b}$ for two firms; price $P^* = \frac{a+2c}{3}$. For $n$ firms: $P \rightarrow c$ as $n \rightarrow \infty$ (convergence to a competitive market). Application: oil industry, aviation (choice of capacities/flights).

Bertrand Model (competition by price): Firms choose price; buyers go to the cheaper one. For a homogeneous product, equilibrium: $P = c$ (competitive price!)—the “Bertrand Paradox.” Two firms are enough for a competitive market. Application: online airline ticket market, bank deposits, market for goods with zero variable costs (software).

Stackelberg Competition: The leader firm first chooses $q_1$, the follower–observer chooses $q_2$ knowing $q_1$. SPNE: leader $q_1^* = \frac{a-c}{2b}$ (greater than Cournot!), follower $q_2^* = \frac{a-c}{4b}$. Leader advantage: the first move yields higher output and profit.

Entry Barriers and the Threat of Entry

Limit Pricing Game: The monopolist threatens a price war upon entry. But: if the price war is unprofitable for the monopolist → the threat is not credible → SPNE predicts entry. The monopolist can reliably commit to war only through irreversible investments (excess capacity, patents, long-term contracts)—then war becomes advantageous.

Numerical Example: The monopolist can “deter” entry if: $\pi_{\text{monopoly}} > \pi_{\text{war, entry}}$ plus the cost of irreversible investments. If the monopolist invests 50 in excess capacity, the price war costs him 20 (loss), for the entrant—30. Then the threat is credible, entry is blocked.

Industry Strategy: Competitor Matrix

Companies use game theory to analyze the competitive environment. The tool—a matrix of strategic interactions:

Situation: two companies choose: invest in R&D (high costs, but advantage) or do not invest.

Nash equilibrium: (R&D, R&D) with payoff (2,2). Although (No R&D, No R&D) is better for both (4,4)—the prisoner’s dilemma! The industry spends on R&D more than “optimal” from a societal point of view.

Negotiations via Game Theory: Rubinstein Model

Alternating Offers (Rubinstein, 1982): Player 1 offers a division of a “pie” $(s, 1-s)$. If Player 2 rejects—it makes a counter-offer (with discounting $\delta_1$, $\delta_2$). Backward induction → SPNE:

$ x^* = \frac{1 - \delta_2}{1 - \delta_1\delta_2} $

—Player 1’s share. If $\delta_1 = \delta_2 = \delta$: $x^* = \frac{1}{1+\delta}$. As $\delta \rightarrow 1$: $x^* \rightarrow 1/2$ (equal division).

Practical conclusion: The more patient party (higher $\delta$) receives a larger share. “Patience is power” in negotiations. The principal, setting a deadline, raises the opponent’s $\delta$ → forces greater concessions.

Auctions in Practice: Frequency Trading Design

In 1994, the US sold mobile communication frequencies in a “simultaneous ascending auction” (SAA): several frequency lots are sold in parallel bidding rounds. Winners pay their final bid. Designer—Paul Milgrom (Nobel 2020).

Problem: Frequencies in adjacent territories are complements (“coverage zone” needed). SAA allows participants to strategically form packages. Result: $7$ billion in revenue in 1994. Since then, more than 40 countries have adopted similar mechanisms.

Pollution and CO₂ Quota Trading (EU ETS): The European Emissions Trading System (EU ETS), a CO₂ emission quota auction. Each firm buys quotas; the quota market equalizes the marginal costs of reducing emissions. VCG logic optimality: firms with low reduction costs reduce emissions, sell quotas; those with high costs buy. Minimizing overall abatement costs for CO₂.

Game Theory in Strategic Management and Regulatory Policy

The synthesis of game theory and real economics forms the foundation of strategic management. Cournot competition (outputs) describes markets with high entry barriers and long production cycles: metallurgy, oil refining, aircraft manufacturing. Bertrand competition (prices)—markets with instantly copyable products: bank deposits, airline tickets on standard routes, retail trade. “Price war” as SPNE explains why low-margin industries with a few players (supermarkets, internet providers) are chronically unprofitable under fierce price competition. Regulatory policy employs game theory in designing antitrust measures: separate accounting (vertically integrated companies), infrastructure access rules (network access for competitors)—all of this changes the structure of the game, shifting equilibrium from monopoly to competitive. Rubinstein negotiations explain why labor disputes (union negotiations with employers) drag on: the lower the union’s discount (workers have a reserve fund)—the greater their demands. Contract theory (principal–agent) is another application: how to structure incentives (bonuses, options) with asymmetric information about productivity.

Assignment: (a) Two airlines compete by price (Bertrand) on the Moscow–St. Petersburg route. With $c = 1000$ rubles/passenger: find the equilibrium price in the Bertrand model. If the route is differentiated (brand loyalty), price competition is less acute—why? (b) Industry investments in R&D—a prisoner’s dilemma. What real mechanisms allow industries to avoid an “arms race”? Name three. (c) Negotiations: for $\delta_1 = 0.9$ and $\delta_2 = 0.7$ (Rubinstein model): calculate the SPNE division of the “pie”. Who benefits from higher discounting?