Game theory: strategic interaction

Detail

1. What game theory studies

• Game theory is the study of strategic interaction. In a strategic interaction, what you get depends on your own choice and also on what others choose.
• Where it is used:
• Oligopoly (a market with a few large sellers, such as cement, telecom or tyres). Each firm watches its rivals before it sets a price.
• Bargaining, for example over wages or a business deal.

• International negotiations, such as trade talks and climate talks.

• Contrast with perfect competition: a perfectly competitive firm is a price taker (it cannot change the market price). So it has no rival to "play against", and strategy does not matter. Game theory becomes useful only when there are few players who depend on each other, as in oligopoly.

• Origins: game theory won the 1994 Nobel Prize in Economics. It was shared by John Nash, John C. Harsanyi and Reinhard Selten for their "pioneering analysis of equilibria in the theory of non-cooperative games" [6].
• A non-cooperative game is one where players cannot sign binding agreements. Each player decides for themselves.

2. Elements of a game

Every game has three parts:

Element	Meaning	Cement example
Players	the people or firms who decide	Firm A, Firm B
Strategies	the choices open to each player	keep the high price / cut the price
Payoffs	what each player gets from each combination of choices	profit in ₹ crore

• A payoff matrix is a table that shows the payoffs for every combination of strategies. By convention, the payoff is written as (row player, column player).

3. Types of games by total payoff

Zero-sum game

• In a zero-sum game, one side's gain exactly equals the other side's loss. Total payoffs always add to zero.
• Formula: Payoff(A) + Payoff(B) = 0 in every cell.
• Examples: poker, fixed-pie bargaining (splitting a fixed sum).
• Worked example: two traders split a fixed ₹100 crore contract.
• If A's share rises from ₹50 crore to ₹60 crore, B's share falls from ₹50 crore to ₹40 crore.
• A's gain (+10) equals B's loss (−10), so the net change is 0.
• Nothing new is created. Value only moves from one side to the other.

Positive-sum game

• In a positive-sum game, cooperation can make the total bigger, so all players can gain at once.
• Examples: voluntary trade, joint research.
• Worked example: India sells software worth ₹100 to a buyer who values it at ₹130. It costs India ₹70 to make.
• The seller gains ₹30 (100 − 70) and the buyer gains ₹30 (130 − 100).

• Total gain = ₹60, and both sides are better off.

• Mercantilism was the 16th–18th century belief that a nation grows rich by exporting more and importing less. It wrongly treated trade as zero-sum. It assumed one country's gain must be another's loss.

• Exam trap: the prisoner's dilemma is not zero-sum. The payoffs in (Keep, Keep) add to 20 and those in (Cut, Cut) add to 10, so the total changes with the players' choices.

4. Dominant strategy

• A dominant strategy is a strategy that gives a player the best payoff whatever the others choose.
• How to test it:
• Fix the rival's choice. Find your best reply.
• Repeat this for every choice the rival could make.

• If the same strategy is best every time, it is dominant.

• Not every game has a dominant strategy. But when a player has one, a rational player will always use it.

5. Nash equilibrium

• Nash equilibrium (John Nash, 1950; Nobel 1994 with Harsanyi and Selten [6]): a set of strategies where no player can gain by changing strategy alone, given what the others are doing.

• Put simply, each player is already making their best reply to the others. Nobody regrets their choice.

• How to check any cell: ask each player, "If I alone switch, do I earn more?" If the answer is "no" for every player, that cell is a Nash equilibrium.

• A Nash equilibrium need not be efficient.
• "Efficient" (Pareto-efficient) means no other outcome makes someone better off without making anyone worse off.

• The prisoner's dilemma below shows a Nash equilibrium that is worse for everyone.

• Relationship to remember: if every player has a dominant strategy, playing those strategies is a Nash equilibrium. The reverse is not true. A game can have a Nash equilibrium with no dominant strategies.

6. Prisoner's dilemma

• Prisoner's dilemma: each player acts in rational self-interest and defects (breaks cooperation). Both end up worse off than if they had cooperated.
• Origin: the game was first framed around 1950 by Merrill Flood and Melvin Dresher [7].
• Why it matters: it explains why cartels are unstable.
• A cartel is a group of firms that agree to fix prices, limit output or share markets, instead of competing.

Payoff matrix. Two cement firms (A, B) choose between keeping the high cartel price and cutting it. Profits are in ₹ crore, shown as (A, B).

	B: Keep high price	B: Cut price
A: Keep high price	(10, 10)	(2, 15)
A: Cut price	(15, 2)	(5, 5)

Reading the matrix, step by step

• Step 1: A's best reply.
• If B keeps the high price, A gets 10 by keeping and 15 by cutting. Cutting is better (15 > 10).
• If B cuts, A gets 2 by keeping and 5 by cutting. Cutting is better (5 > 2).

• So cutting is A's dominant strategy.

• Step 2: B's best reply. The game is symmetric (the same for both), so cutting is B's dominant strategy too.

• Step 3: Nash equilibrium. The result is (Cut, Cut) = (5, 5).

• Check: if A alone switches to Keep, A gets 2, which is less than 5. B faces the same choice. So neither firm moves.

• Step 4: Compare with cooperation. (Keep, Keep) = (10, 10) is better for both firms.

• Joint profit is 20 under cooperation and only 10 in the equilibrium.

• But (Keep, Keep) is not stable, because each firm can earn 15 by cheating.

• Lesson: individual rationality leads to a collectively irrational result.

• Gain from cheating: 15 − 10 = ₹5 crore. This is the temptation that breaks cartels.
• Consumer angle: from society's point of view, the "bad" equilibrium for the firms (low prices) is good for buyers. Competition law aims to keep firms in this equilibrium.

7. Applications

(a) Cartel cheating and leniency: India's lesser penalty regime

• Leniency makes "confess first" the dominant strategy, because the first firm to report the cartel gets the largest cut in its penalty.
• Legal basis in India:
• Section 46 of the Competition Act, 2002, read with the CCI (Lesser Penalty) Regulations [2].

• The Competition Commission of India (CCI) is the regulator that enforces the Act.

• Cartels are illegal under Section 3:

• Section 3(1) bans anti-competitive agreements.

• Section 3(3) covers horizontal agreements (agreements between rivals), including bid-rigging under Section 3(3)(d) [5].

• Old and new rules:

• The CCI (Lesser Penalty) Regulations, 2024 were notified on 20 February 2024. They replaced the 2009 regulations [2].
• The Competition (Amendment) Act, 2023 added "Lesser Penalty Plus" (LPP) under Section 46 [2].
• Under LPP, a firm that has already applied for leniency in one cartel gets an extra penalty cut if it reports another cartel that the CCI did not know about [2].

• Game-theory logic: LPP makes every cartel a firm belongs to a possible "confession" game. This raises the risk of forming cartels.

• CCI enforcement: the CCI investigated 35 cartel cases in the five years covered by a 2025 PIB release [2].

• Leniency works in order of confession. Case examples:

Case	1st applicant	2nd	3rd	Source
Zinc-carbon dry cell batteries	Panasonic: 100% reduction	Eveready: 30%	Nippo: 20%	[3]
Maritime transport (car carriers)	NYK Line: 100%	MOL: 50%	NMCC: 30%	[4]

• Notice that the first confessor gets the biggest reward. This creates a race to confess, which is exactly the prisoner's dilemma logic.

• Illustrative leniency matrix (penalty cost in ₹ crore, lower is better; numbers are illustrative):

	B: Stay silent	B: Confess
A: Stay silent	(0 if never caught, but risky)	(−100, 0)
A: Confess	(0, −100)	(−50, −50)

• Whatever B does, confessing reduces A's expected loss. So confessing is dominant, and the cartel falls apart.

• Cement sector example (bid-rigging): the CCI penalised 7 cement companies for bid-rigging in a 2012 tender floated by the Director, Supplies & Disposals, Haryana [5].

• The firms included UltraTech (₹68.30 crore), Jaiprakash Associates (₹38.02 crore), Ambuja (₹29.84 crore) and ACC (₹35.32 crore) [5].
• The penalty was set at 0.3% of average turnover over the preceding three years [5].
• The violation was Section 3(3)(d) read with Section 3(1) [5].

(b) Arms races

• Both sides arm, and neither is safer.
• "Arm" is each country's dominant strategy, because being unarmed while the rival arms is the worst outcome.
• Result: both spend heavily and security does not improve.

(c) Price wars and tariff wars

• Retaliatory tariffs leave both countries poorer, as in the US-China tariff rounds.
• Each country gains a little by protecting its own industry.

• When both do it, trade shrinks and both lose.

• Link to WTO: the Most-Favoured-Nation (MFN) rule (a country must treat all WTO members equally on tariffs) and binding tariff ceilings work as a rule that helps members cooperate.

(d) Climate negotiations

• Each country prefers others to cut emissions, which is free riding on a global public good.
• Public good: it is non-excludable (you cannot stop anyone from using it) and non-rival (one person's use does not reduce what others get). A stable climate is an example.
• Free riding means enjoying the benefit without paying the cost.
• Each country thinks: "If others cut, I benefit anyway. If they don't, my cut alone won't help." So each country delays its own cut.

(e) Fisheries (tragedy of the commons)

• Every boat over-fishes (links to Section 7).
• Each boat gains from an extra catch, but the loss to fish stocks is shared by everyone.
• Result: the fishery collapses, even though every boat owner would prefer a healthy one.

8. The way out: repeated games

• One-shot game vs repeated game:
• In a one-shot game, the game is played once. Defection wins.

• In a repeated game, the same game is played again and again. When it repeats without end, the threat of future punishment can sustain cooperation.

• Worked example (using the cement matrix, 3 rounds, no discounting):

• Always cooperate: 10 + 10 + 10 = 30.
• Cheat in round 1, then the rival punishes by cutting forever: 15 + 5 + 5 = 25.
• Since 30 > 25, cheating does not pay once punishment is expected. Over more rounds, the gap grows (for example, 100 vs 60 over 10 rounds).

• Catch: if both firms know the last round, they cheat in it. Working backwards, cooperation unravels. So cooperation needs an uncertain or infinite end.

• Tit-for-tat:

• Rule: cooperate in the first round, then copy the rival's last move.
• Axelrod's tournaments: in 1980, political scientist Robert Axelrod ran round-robin tournaments. In them, computer programs played repeated prisoner's dilemmas with no definite end [7].
• Tit-for-tat won [7].

• Why it works: it is simple, forgiving and does well in repeated play.

  • Nice: it never cheats first.
  • Retaliatory: it punishes cheating at once.
  • Forgiving: it returns to cooperation as soon as the rival does.
  • Clear: the rival easily understands it.

• Tacit collusion: this is why tacit collusion survives in stable oligopolies.

• Tacit collusion means firms keep prices high without any written or spoken agreement. They simply follow each other's prices.
• It survives where there are few firms, prices are easy to see and the market is stable.
• Policy problem: competition law needs proof of an "agreement". Tacit collusion is hard to prosecute, so regulators rely on market studies and on leniency applicants.

Prelims Hooks

• Nash equilibrium: no player can gain by changing strategy alone. It need not be Pareto-efficient (a common trap).
• 1994 Nobel Prize in Economics: Nash, Harsanyi and Selten, for equilibria in non-cooperative games [6].
• Dominant strategy: best whatever the rival does. In the prisoner's dilemma, "defect/cut price" is dominant for both players.
• The prisoner's dilemma is NOT a zero-sum game. The total payoff changes with the players' choices (20 vs 10 in the cement example).
• Mercantilism wrongly treated trade as a zero-sum game. Voluntary trade is positive-sum.
• Leniency in India: Section 46, Competition Act, 2002, with the CCI (Lesser Penalty) Regulations, 2024, which replaced the 2009 regulations [2].
• "Lesser Penalty Plus" came from the Competition (Amendment) Act, 2023. It gives an extra cut for disclosing a second, unknown cartel [2].
• Bid-rigging is a cartel offence under Section 3(3)(d) of the Competition Act [5].
• Tit-for-tat (cooperate first, then copy the rival) won Axelrod's 1980 tournaments of repeated prisoner's dilemmas [7].
• Free riding on a global public good (climate) is a prisoner's dilemma among nations.

Mains Points

• Why cartels break, and how law uses this:
• Cartels are unstable because cheating is each member's dominant strategy.
• India's lesser penalty regime (Section 46; 2024 Regulations; LPP under the 2023 amendment) deliberately turns silence into a losing strategy [2].
• The graded rewards (100% / 50% / 30% in the maritime case) create a race to confess [4].

• Useful in GS-III answers on competition policy and ease of doing business.

• Tacit collusion is the limit of enforcement:

• In concentrated sectors such as cement, repeated interaction supports high prices without an explicit agreement.
• This is hard to prove under Section 3.

• Suggested fixes: market studies, price-transparency rules, merger scrutiny of consolidation, and evidence from leniency applicants.

• Global commons and trade as prisoner's dilemmas:

• Climate talks and tariff wars show why self-interested nations end up in bad equilibria.
• Institutions such as the WTO (MFN rule, dispute settlement) and the UNFCCC (national pledges with review) act as "repeated game" devices. They reward cooperation and make defection visible.

• Usable in GS-II (international institutions) and GS-III (environment).

• Efficiency vs rationality:

• A Nash equilibrium can be individually rational yet socially wasteful (over-fishing, arms races).
• This is a key argument for state regulation in cases of market failure (quotas, pollution standards, competition law) instead of relying only on the market.