Game theory is the formal tool for analysing strategic interaction — situations where each agent's optimal action depends on what other agents do. Most realistic economic environments (oligopoly pricing, cartel sustainability, international trade negotiations, household-level bargaining) involve strategic interaction. Game theory is the toolkit.
The basic structure of a game
- Players — who is making decisions
- Strategies — what choices each player has
- Payoffs — what each player gets for each combination of strategies
- Information — what each player knows about the game
- Timing — simultaneous or sequential moves
The prisoner's dilemma
Two suspects are arrested. Each can confess (defect) or stay silent (cooperate). If both stay silent, both get light sentences (say, 1 year each). If both confess, both get heavy sentences (5 years each). If one confesses and the other stays silent, the confessor goes free and the silent one gets 10 years.
Player 2: Stay silent Player 2: ConfessPlayer 1:Stay silent (-1, -1) (-10, 0)Confess (0, -10) (-5, -5)Reading: (Player 1 payoff, Player 2 payoff). Negative = jail time.
Each player's dominant strategy is to CONFESS. Whatever the other player does, confessing is better for you. So both confess → both get 5 years, even though both could have gotten 1 year by cooperating. The Nash equilibrium (both confess) is INFERIOR to the cooperative outcome (both stay silent). This is the prisoner's dilemma — individually rational behaviour produces collectively suboptimal outcomes.
Nash equilibrium
Nash equilibrium definition
A Nash equilibrium is a set of strategies (one per player) such that no player can improve their payoff by unilaterally changing their strategy, given the strategies of the other players. In other words: at NE, each player is playing a best response to the others' strategies. Nash equilibrium can be: • Pure strategy (each player picks one action with certainty) • Mixed strategy (players randomise among actions) Most games have at least one Nash equilibrium (Nash's existence theorem, 1950). Many have multiple — selecting which one will be played requires additional argument (focal points, dynamics, evolutionary refinement).
Coordination games
Different shape from prisoner's dilemma. Players want to coordinate on the same outcome, but there are multiple ways to coordinate.
Player 2: Go left Player 2: Go rightPlayer 1:Go left (5, 5) (0, 0)Go right (0, 0) (5, 5)Two Nash equilibria: (Left, Left) and (Right, Right). Both are coordinationoutcomes. The challenge: which one will players coordinate on?Focal-point effects (Schelling) often resolve this — driving on theright in the US, on the left in Kenya. The convention is the focalpoint that allows coordination.
Repeated games and reputation
When players interact over and over, cooperative outcomes that aren't Nash equilibria in the one-shot game become sustainable. In the repeated prisoner's dilemma, the strategy 'cooperate as long as the other player cooperated last period; defect if they defected last period' (tit-for-tat) can sustain cooperation. Each player knows defecting today triggers retaliation tomorrow, which makes today's defection unprofitable.
Folk theorem
In an infinitely-repeated game with sufficiently patient players, any individually-rational outcome is sustainable as a Nash equilibrium. 'Sufficiently patient' means players value future payoffs enough to forgo a one-shot defection gain. The folk theorem explains why cooperation arises in real-world repeated interactions — between trade partners, neighbours, repeat customers and suppliers, cartel members. The threat of future retaliation enforces what would otherwise be unenforceable. Key implication for African markets: where formal contract enforcement is weak, repeated-game cooperation can substitute. Long-term supplier-buyer relationships, reputation-based trade networks, ethnic-based business networks all exploit the folk theorem mechanism.
Cournot oligopoly
Each firm chooses output, price clears the market given total industry output. With two firms (duopoly):
Cournot duopoly solution
Linear-demand example: P = a − b(q₁ + q₂) Each firm's profit: π_i = q_i × [a − b(q₁ + q₂)] − c × q_i where c = marginal cost. Firm 1's best-response function (given firm 2's output q₂): q₁ = (a − c − bq₂) / (2b) Firm 2's best-response function (given firm 1's output q₁): q₂ = (a − c − bq₁) / (2b) Solving simultaneously (using symmetry q₁ = q₂ = q*): q* = (a − c) / (3b) Q_industry = 2q* = 2(a − c) / (3b) Compare: • Monopoly: Q_m = (a − c) / (2b) • Cournot duopoly: Q_d = 2(a − c) / (3b) = (4/3) × Q_m • Perfect competition: Q_pc = (a − c) / b = 2 × Q_m Cournot output sits between monopoly and competitive. Welfare loss is smaller than monopoly but real.
Bertrand competition
Firms choose prices (not quantities). With homogeneous products, the lower-price firm captures the whole market. Equilibrium: P = MC for both firms — same as perfect competition. The 'Bertrand paradox': just two firms is enough for marginal-cost pricing if they're price-setters with identical products. Real-world Bertrand is more nuanced because of differentiation, capacity constraints, and repeated interaction.
Application: East African cement market
East Africa cement has historically been a four-firm oligopoly (Bamburi, East African Portland, Mombasa Cement, Tororo Cement). With moderate product differentiation (some quality variation), modest capacity constraints, and substantial transport costs creating regional sub-markets, the market behaves closer to Cournot than Bertrand.
The 2010s entry of Dangote (Nigerian-based) and ARM Cement expansion disrupted the equilibrium. Capacity expansion led to price competition; some incumbents struggled. The episode illustrates how supply-side shocks alter strategic-interaction equilibria.
Application: airline yield management
Airlines (Kenya Airways, foreign carriers) practice yield management — selling the same seat at different prices to different customers based on timing, advance-purchase, fare class. This is third-degree price discrimination informed by game theory: airlines anticipate that price-sensitive customers will book early at low fares, that business customers will book late at high fares, and structure fare classes accordingly to segment the demand.
Application: cartel sustainability
OPEC, banking cartels (rate-fixing scandals), price-fixing in commodity sectors. The economic question: why do cartels form and why do they break?
- Formation — repeated game; high payoff to cooperation; concentrated market; sustainability conditions met
- Maintenance — monitoring of compliance; sanctions for cheating; barriers to entry preventing new firms from eroding rents
- Breakdown — cheating temptation rises when cooperation gain is shared among more participants; entry by new firms erodes incumbents' rent; demand shocks reduce incumbent's stake in the cooperative outcome
Kenya banking has been investigated multiple times for collusion on lending rates (e.g., the SBM/HF saga around 2010). Forensic-economics work suggests informal coordination on rate-setting was substantial during periods. Implementation of consumer-protection rules, regulatory oversight, and entry by digital lenders has reduced (not eliminated) this coordination.
Exercise
Two major Kenyan banks (Bank A and Bank B) are deciding whether to raise their personal-loan rates by 2 percentage points. Each can RAISE or KEEP rates unchanged. If both raise, both gain higher margins on each loan but lose some customers to other banks. If neither raises, both keep current customers but margins remain compressed. If only one raises, that bank loses customers to the other. The estimated payoffs (annual profit in KES millions): Bank B: Keep Bank B: Raise Bank A: Keep (500, 500) (800, 200) Raise (200, 800) (650, 650) (1) Find the Nash equilibrium(s) of this one-shot game. (2) Is the equilibrium Pareto-optimal? (3) Suppose this game is played every quarter for many years. What strategy would sustain the cooperative outcome (both raise)? (4) What does this tell us about why coordinated bank-rate increases can persist?