Lecture 5: Game Theory Applied — Strategic Design in Politics, Evolution, and Economics

Game Theory Series — Summary

Lecture	Core Concepts	Key Insight
1	Prisoner’s Dilemma, Nash Equilibrium	Individual rationality ≠ collective optimum
2	Mixed Strategies, Multiple Equilibria	Unpredictability is strategy; focal points select equilibria
3	Repeated Games, Tit-for-Tat	Repetition enables cooperation
4	Auction Theory, Winner’s Curse	Information is the ultimate bidding weapon
5	Applications — Politics, Evolution, Signaling	Applicable to all strategic interactions

Signaling Games

In situations of information asymmetry, one side sends a signal to reveal their type.

Structure of Signaling Games
Sender	Signal	Receiver's Interpretation	Real-World Example
High-ability job seeker	Earn a degree from a top university	Signal of high ability	Education signaling theory (Spence)
High-quality firm	Invest heavily in advertising	Signal of long-term viability	Brand advertising
Financially strong firm	Pay dividends	Signal of free cash flow	Stock price reacts positively
Powerful military	Public military exercises	Signal that war would be costly	Deterrence effect

For a signal to be credible, it must be costly to imitate. It must be unprofitable for a low-type player to send the same signal. For example, a top-tier degree is relatively easy for a high-ability person to obtain, but too costly for a low-ability person — so the low-ability person won’t imitate it.

Evolutionarily Stable Strategy (ESS)

The intersection of biological evolution and game theory — a concept developed by John Maynard Smith:

Hawk-Dove Game — Evolutionarily Stable Strategy
Strategy	vs. Hawk	vs. Dove	Characteristics
Hawk (Aggressive)	Both injured (-25, -25)	Monopolizes resource (+50, 0)	Aggressive, high-risk
Dove (Passive)	Concedes (0, +50)	Splits resource (+15, +15)	Passive, low-risk

Evolutionarily Stable Strategy (ESS):
→ A state where no invading strategy can spread through the population
→ All-Hawk population: Doves can invade (peaceful doves earn high returns)
→ All-Dove population: Hawks can invade (aggressive hawks monopolize)
→ Mixed ESS: Hawks at proportion p*, Doves at (1-p*) coexist

Real-World Applications:
→ Explains coexistence of competing species
→ Hawks vs. doves ratio within organizations
→ Balance of aggressive vs. defensive firms in markets

Moral Hazard and Mechanism Design

Problems Created by Information Asymmetry
Problem Type	Structure	Solution	Example
Adverse Selection	Information asymmetry before the transaction	Signaling, screening, warranties	Lemons market (used cars)
Moral Hazard	Behavior unobservable after the transaction	Performance pay, monitoring, co-payments	Carelessness after getting insurance
Principal-Agent Problem	Does the agent's interest align with the principal's?	Incentive design	Executive stock options

What Is Mechanism Design?

Reverse game theory — designing the rules of the game itself so that the desired outcome becomes the Nash Equilibrium. It's the perspective of the 'rule-maker.'

Incentive Compatibility

Design the system so that each participant's best interest is to reveal their true type. The Vickrey auction is the canonical example.

Real-World Applications

Tax filing systems, school exams, physician fee schedules, platform review systems — all are products of mechanism design.

Limitations

Perfect incentive design is impossible. Unexpected strategic responses always emerge, requiring continuous redesign.

The Voting Paradox and Political Game Theory

The Voting Paradox — Condorcet's Paradox
Voter	1st Choice	2nd Choice	3rd Choice
Voter A (1/3)	Policy X	Policy Y	Policy Z
Voter B (1/3)	Policy Y	Policy Z	Policy X
Voter C (1/3)	Policy Z	Policy X	Policy Y

Pairwise Majority Voting:
X vs Y → X wins (A+C prefer X)
Y vs Z → Y wins (A+B prefer Y)
Z vs X → Z wins (B+C prefer Z)

→ X > Y > Z > X (collective preference is intransitive)
→ The agenda-setter can manipulate voting order to produce any desired outcome

Median Voter Theorem:
→ In one-dimensional policy competition, the party that wins the median voter wins the election
→ Explains why US two-party politics tends to converge toward the center

Limitations of Game Theory and Behavioral Extensions

Standard Game Theory's Limitations and Behavioral Game Theory Corrections
Standard Assumption	Departure from Reality	Behavioral Game Theory Correction
Perfect Rationality	Cognitive biases, emotional decisions	Bounded rationality models
Self-interested Preferences	Fairness preferences, anger responses	Inequality aversion models
Common Knowledge	Differences in information processing capacity	Cognitive hierarchy model (k-level thinking)
Equilibrium Reached Instantly	Learning and time required	Evolutionary games, reinforcement learning

Game theory systematizes the fact that “the other party is also thinking strategically.” It operates in every negotiation, business decision, political contest, and daily interaction. The core question: “What are their incentives? Given those incentives, how will they behave? How should I design my own strategy in response?”

Comprehensive Key Takeaways

Signaling games: only costly signals are credible — impossible to imitate = truthful revelation Moral hazard: align agent’s incentives with principal’s through incentive design Mechanism design: design the rules so the desired outcome becomes the Nash Equilibrium Voting paradox: agenda order determines outcome — the rule-setter is the real power