BUSS1040 · Economics For Business Decision Making
Strategic Interaction I: Simultaneous Games
Topic 7 starts strategic interaction with simultaneous games: players choose at the same time, so you reason from a payoff matrix. The two examinable tools are the dominant strategy (a best choice regardless of the opponent) and the Nash equilibrium (best response to best response, no profitable unilateral deviation). The flagship application is the prisoner's dilemma, where individually rational choices yield a worse joint outcome. It is examined as short-answer and MCQ: identify dominant strategies, find the Nash equilibrium(s), and recognise dilemma/coordination structures.
What this chapter covers
- 011. Simultaneous games and the payoff matrix (first payoff = row player, second = column)
- 022. Best response: the highest-payoff choice given what the other player does
- 033. Dominant strategy: a best response regardless of the opponent's choice
- 044. Iterated elimination of dominated strategies
- 055. Nash equilibrium: a strategy pair where neither can gain by deviating alone
- 066. The prisoner's dilemma: dominant strategies produce a Pareto-inferior outcome
- 077. Coordination games and games with multiple Nash equilibria
- 088. Business applications: price-fixing, advertising and entry games
Dominant strategy and Nash equilibrium in a pricing game
- 2 marksFirm 1's best responses: if Firm 2 plays H, Firm 1 gets 6 (H) vs 8 (L) ⇒ Low; if Firm 2 plays L, Firm 1 gets 2 (H) vs 4 (L) ⇒ Low. Low is best in both cases ⇒ Low is dominant for Firm 1.
- 1 markBy symmetry, Firm 2 also has Low as a dominant strategy (it earns more by playing Low whatever Firm 1 does).
- 2 marksThe Nash equilibrium is where both play their best response simultaneously: (Low, Low) with payoffs (4, 4). Neither can gain by switching to High alone.
- 1 markClassify: both would be better off at (High, High) = (6, 6), but each has a dominant incentive to undercut — this is a prisoner's dilemma.
Key terms
- Payoff matrix
- A grid showing each player's payoff for every combination of strategies. By convention the first number in a cell is the row player's payoff and the second is the column player's.
- Best response
- A player's payoff-maximising strategy GIVEN the strategy of the other player. Finding best responses cell by cell is the mechanical route to a Nash equilibrium.
- Dominant strategy
- A strategy that is a best response no matter what the opponent does. If a player has a dominant strategy they will play it, which can pin down the equilibrium immediately.
- Nash equilibrium
- A combination of strategies in which each player's choice is a best response to the others', so no one can gain by unilaterally deviating. A game can have one, several, or no pure-strategy Nash equilibria.
- Prisoner's dilemma
- A game in which each player has a dominant strategy, but both playing it yields an outcome worse for everyone than mutual cooperation. It captures why cartels, price-fixing and arms races are individually rational yet collectively bad.
- Coordination game
- A game with multiple Nash equilibria where players want to match choices (e.g. both adopt the same standard). The challenge is coordinating on which equilibrium, not whether to cooperate.
Strategic Interaction I: Simultaneous Games FAQ
How do I find the Nash equilibrium from a payoff matrix?
Use the best-response method. For the row player, go column by column and underline (or mark) their highest payoff in each column. For the column player, go row by row and mark their highest payoff in each row. Any cell where BOTH payoffs are marked is a pure-strategy Nash equilibrium — neither player can do better by deviating alone. A game may have one, more than one, or no pure-strategy Nash equilibrium, so check every cell.
What is the difference between a dominant strategy and a Nash equilibrium?
A dominant strategy is about ONE player: it is their best choice regardless of what the opponent does. A Nash equilibrium is about the OUTCOME: a strategy combination where every player is best-responding simultaneously. If a player has a dominant strategy, it must be part of any Nash equilibrium — but plenty of Nash equilibria exist in games with no dominant strategy at all (e.g. coordination games), so the two concepts are not the same.
Why is the prisoner's dilemma outcome 'bad' if it is a Nash equilibrium?
Because Nash equilibrium only requires that no one can improve by deviating ALONE — it says nothing about whether the outcome is jointly efficient. In the dilemma, each player's dominant strategy (defect / set Low / undercut) leads to a cell that is worse for BOTH than mutual cooperation, yet neither can unilaterally move to the better cell without being exploited. That gap between individual rationality and collective benefit is exactly why it models cartels, advertising wars and environmental over-use.
How is Topic 7 examined?
As short-answer and MCQ on simultaneous games: identify each player's dominant strategy (if any), find the Nash equilibrium/equilibria by best responses, and recognise the structure (prisoner's dilemma, coordination, etc.). You may be asked to interpret a business scenario — a price-fixing, advertising, or capacity game — as a payoff matrix and explain why the equilibrium differs from the cooperative outcome. Topic 8 then extends this to sequential games and oligopoly.
Exam move
Always solve a simultaneous game mechanically rather than by intuition: mark the row player's best response in each column and the column player's best response in each row, and any doubly marked cell is a Nash equilibrium. Check for dominant strategies first — if one exists it collapses the analysis fast. Learn to name the structure, because examiners reward it: a prisoner's dilemma (dominant strategies, jointly worse outcome), a coordination game (multiple equilibria), or a game with no pure-strategy equilibrium. Practise translating business stories (cartels, advertising, entry) into a payoff matrix, and rehearse the one-line explanation of why the Nash outcome can be collectively inefficient — that sentence is the bridge into repeated games in Topic 8.
