Game Theory and Strategic Thinking Notes (chapyer 9 week 2)

Learning Objectives

LO 9.1: Understand strategic behavior and describe the components of a strategic game.
LO 9.2: Explain why noncooperation is always the outcome in the prisoner's dilemma.
LO 9.3: Identify whether or not a player has a dominant strategy in a one-time game.
LO 9.4: Identify whether or not a Nash equilibrium will be reached in a one-time game.
LO 9.5: Explain how a commitment strategy can be used to achieve cooperation in a one-time game.
LO 9.6: Explain how repeated play can enable cooperation.
LO 9.7: Explain how backward induction can be used to make decisions.
LO 9.8: Use a decision tree to solve a sequential game.
LO 9.9: Define first-mover advantage and identify it in practice.
LO 9.10: Explain why patient players have more bargaining power in repeated games.
LO 9.11: Explain how a commitment strategy can allow players to achieve their goals by limiting their options.

Introduction: The Littering Problem

**The Paradox:** Everyone prefers a clean environment, but individual incentives often lead to littering.
**Escalation:** One person's litter encourages others to litter, leading to a dirtier environment.
**Solution Attempts:**-
**Norms:** Creating strong social norms against littering (e.g., "Don't mess with Texas" campaign).
**Economic Incentives:** Using fines and public humiliation (e.g., Singapore's strict anti-littering laws).
**Singapore's Approach:**-
Fines of $1,400$ for littering.
Corrective work orders involving public trash collection in bright vests.
Higher penalties for larger dumping offenses (up to $35,000$ in fines, a year in jail, and vehicle forfeiture).
**Comparison to New York City:** Lower fines ( $50$ to $250$ ) and less convenient trash disposal.
**International Challenges:** Difficult to address trash moving across borders or in international waters.
**Prisoner's Dilemma:** The littering problem exemplifies the prisoner's dilemma, where rational choices lead to a suboptimal outcome for all.

Games and Strategic Behavior

**Game Theory:** The study of how people behave strategically under different circumstances.- A "game" is any situation involving at least two people requiring strategic thinking.
#### Strategic Behavior
**Rational Behavior:** Making decisions by considering trade-offs and pursuing goals effectively.
**Strategic Behavior:** Acting to achieve a goal by anticipating the interplay between your own and others' decisions.
**Key Question:** "How will others respond?"
#### Rules, Strategies, and Payoffs
**Rules:** Define allowed actions (e.g., chess piece movements, laws, cost structures for businesses, electoral college).
**Strategies:** Plans of action to achieve goals (e.g., buying cheap properties in Monopoly, producing a certain quantity of goods, using hopeful language in an election campaign).
**Payoffs:** Rewards from particular actions (monetary or nonmonetary) (e.g., salary, winning a game, being elected).

One-Time Games and the Prisoner's Dilemma

**Prisoner's Dilemma:** A situation where two people make rational choices that lead to a less than ideal result for both.
#### Classic Scenario:
Two suspects arrested for a major and minor crime.
Police lack evidence for the major crime but can convict on the minor one.
Deal offered: Confess and implicate the other for a reduced sentence (1 year), while the accomplice gets the maximum (20 years).- If both confess: Both get 10 years.
If neither confesses: Both get 2 years for the minor crime.
**Rational Outcome:** Both confess, resulting in 10 years each, even though cooperating (staying silent) would lead to only 2 years each.
#### Decision Matrix:
Visual representation of possible outcomes based on each player's choices.
#### Presidential Election Campaign Example:
**Strategies:** Go negative or stay positive.
**Payoffs:** Winning easily (top preference), tight race, losing heavily (last choice).
**Outcome:** Both campaigns go negative, damaging reputations and disillusioning voters, even though a positive campaign might be preferable.
#### Littering Game Example:
**Players:** You and your neighbor (representing the community).
**Strategies:** Litter or don't litter.
**Payoffs:** Points assigned to each outcome (relative size matters).

Finding the Dominant Strategy

**Dominant Strategy:** The best strategy to follow, regardless of what other players choose.
**Examples:**-
Confessing in the prisoner's dilemma.
Going negative in the election campaign.
#### Rock, Paper, Scissors:
No dominant strategy exists because the best choice depends on the opponent's play.

Reaching Equilibrium

**Equilibrium:** A state where no individual has an incentive to change their behavior, given what others are doing.
#### Nash Equilibrium:
Reached when all players choose the best strategy they can, given the choices of all other players.
Also described as a situation of "no regrets."
Named after game theorist John Nash.
#### Examples:
**Rock, Paper, Scissors:** No Nash equilibrium.
**Prisoner's Dilemma:** Nash equilibrium is both confessing, even though it's not the best outcome.
**Driving Game:** Multiple equilibria (both drive on the right or both drive on the left).- Driving on the right (or left) is not a dominant strategy, as the best decision depends on what others do.

Avoiding Competition Through Commitment

**Commitment Strategy:** Players agree to submit to a penalty in the future if they defect from a given strategy.
#### Advantages:
Can lead to mutually beneficial equilibrium otherwise difficult to maintain.
#### Disadvantages:
Hard to make work in some contexts.
#### Examples:
**Organized Crime:** Mafia's code of silence (omerta) discourages members from testifying.
**Witness Protection Program:** Increases the payoff for confessing by providing protection.
**Gas Station Price War:** Two stations (Conoco and Exxon) could cooperate to keep prices high, but consumers benefit from competition.
**Collusion:** Cooperation in a business context, often leading to higher prices.- Governments try to prevent collusion to protect consumers.

Repeated Play in the Prisoner's Dilemma

**Repeated Game:** A game played more than once.
**Impact:** Strategies and incentives change; players may reach mutually beneficial equilibria without commitment strategies.
#### Tit-for-Tat Strategy:
Whatever the other player does, you do the same in response.
Effective in repeated prisoner's dilemma-type games.
Leads to lasting cooperation without explicit agreements.
#### Example:
Gas station managers increasing/decreasing prices based on the competitor's actions.
#### Economics in Action: What do price-matching guarantees guarantee?
Price matching might guarantee higher, not lower, prices.
Signals commitment to the "tit for tat" strategy.
Home Depot and Lowe's: Nearly identical price matching policies reduce the incentive to lower prices.
#### Limitations of Tit-for-Tat:
Less effective when games are not repeated indefinitely (e.g., nearing election day).
Less effective when players are primarily concerned with relative payoffs rather than absolute payoffs.
#### Robert Axelrod's Tournament:
Tit-for-tat was the most successful strategy in a repeated prisoner's dilemma game.
#### Econ and You: Can game theory explain why you feel guilt?
Some researchers believe emotions evolved from tit-for-tat games played by ancestors to achieve cooperation.
Emotions like sympathy, gratitude, vengeance, guilt, and forgiveness help sustain cooperation.

Sequential Games

**Sequential Games:** Players make decisions one after the other, rather than simultaneously.
#### Think Forward, Work Backward
**Backward Induction:** Analyzing a problem in reverse, starting with the last choice, then the second to last choice, and so on to determine the optimal strategy.
#### Example:
Choosing courses for the next semester by considering future career goals.
#### Deterring Market Entry: A Sequential Game
Example: McDonald's considering opening a restaurant in a small town.
Factors: Location (center vs. outskirts), rates of return, and the possibility of Burger King also entering the market.
#### Decision tree analysis:
McDonald's evaluates outcomes based on Burger King's potential actions.
McDonald's builds in the center of the town to deter Burger King from entering the market. Burger King would have a low return on investment because McDonald's would already be established.
#### What do you think? Surviving with Strategic Thinking
Example: Richard on Survivor using backward induction to lose a challenge purposefully and win the game.

First-Mover Advantage in Sequential Games

**First-Mover Advantage:** The player who chooses first gets a higher payoff than those who follow.
#### Example:
Negotiation between a company and its employees' labor union over wages.

Repeated Sequential Games

Repeated play can reduce the first-mover advantage.
The ability to make counteroffers transforms bargaining.
A more patient player, who puts more value on future rewards, will have more bargaining power.

Commitment in sequential games

Following a commitment strategy in sequential games can change opponent behavior.
Example - Spanish conquest of Mexico Hernán Cortés burns his ships.
#### Economics in Action: Totally M.A.D.
The Cold War: Mutually Assured Destruction (MAD) strategy.

Conclusion

Game theory provides a framework for analyzing strategic interactions.
Backward induction, considering the rules, strategies, and payoffs in detail, and how to change the rules and constraints to achieve a better outcome helps to find the best outcome.

Key terms

Game p 207 - A situation involving at least two people requiring strategic thinking
Game theory p 207 - The study of how people behave strategically under different circumstances.
Behaving strategically p 207 - Acting to achieve a goal by anticipating the interplay between your own and others' decisions.
Prisoner's dilemma p two hundred seven - A situation where two people make rational choices that lead to a less than ideal result for both.
Prisoner's dilemma p 207 - A situation where two people make rational choices that lead to a less than ideal result for both.
Dominant strategy p 209 - The best strategy to follow, regardless of what other players choose.
Nash equilibrium p 211 - Reached when all players choose the best strategy they can, given the choices of all other players.
Commitment strategy p 212 - Players agree to submit to a penalty in the future if they defect from a given strategy.
Repeated game, p 214 - A game played more than once.
Tick for tat, p 214 - Whatever the other player does, you do the same in response.
Backward induction, p 217 - Analyzing a problem in reverse, starting with the last choice, then the second to last choice, and so on to determine the optimal strategy.
First mover advantage, p 220 - The player who chooses first gets a higher payoff than those who follow.

Summary

L o 9.1 understands strategic behavior and describe the components of a strategic game.
L o 9.2 explain why non cooperation is always the outcome in the prisoner's dilemma.
L o 9.3 identify whether or not a player has a dominant strategy in a one time game.
L o 9.4 identify whether or not a Nash equilibrium will be reached in a one time game.
L o 9.5 explain how a commitment strategy can be used to achieve cooperation in a one time game.
L o