Game Theory and Strategic Thinking - chapter 9

Game: a situation involving at least two people that requires those involved to think strategically
Game theory: the study of how people behave strategically under different circumstances
behaving strategically: acting to achieve a goal by anticipating the interplay between your own and others’ decisions
Games have rules, which define the actions players are allowed to take
Strategies: are plans of action that players can follow to achieve a desired goal
Payoffs: the rewards that come from taking particular actions

Prisoners’ dilemma: a game of strategy in which two people make rational choices that lead to a less-than-ideal result for both
Each player has a choice to cooperate or not to cooperate
Each prefers mutual cooperation to mutual non-cooperation
- But non-cooperation is the best choice because its payoff is higher no matter what strategy other players choose
In this game, pursuing you own self-interest leaves everyone worse off

Dominant strategy: When a strategy is the best one to follow no matter what strategy other players choose
Not all games feature a dominant strategy
- In some games there is no single strategy that will work best for you

When all players choose the best strategy they can, given the choices of all other players, those players have reached a Nash equilibrium
Players who have reached a Nash equilibrium have no reason to regret their decision
- This doesn’t necessarily mean that an equilibrium outcome to a game is a good one
- We can see both negative-negative and positive-positive outcomes in equilibrium
- The only condition is that there’s no incentive to switch from one decision to another

In the prisoners’ dilemma, the players of the game would be better off if they could cooperate and make a deal beforehand not to confess
However, even if you know you accomplices will not confess, you are still better off confessing
To solve the problem, players may sometimes reach a mutually beneficial equilibrium by pursuing a commitment strategy
- Where they agree to submit to a penalty if they defect from the equilibrium

In a repeated game, players can penalize each other for defecting in one round by punishing each other in the next round
As a result, the players can sometimes achieve a mutually beneficial equilibrium, even when they couldn’t do so in a single game
A common strategy in repeated games is tit-for-tat, in which a player takes the same action as their opponent in the previous round
Anyone who is playing against a person with a tit-for-tat strategy has a strong incentive to cooperate because defecting would push them into a less profitable equilibrium in every future round of the game

Backward induction is the process of analyzing a problem in reverse
- Starting with the last choice, then the second to last choice, etc
This problem-solving tool can be used to choose between options with different consequences down the road
- You first choose the goal you are trying to reach and then determine the steps needed to reach it

In many situations, one person or company must make a decision before the other one
- These situations can be represented as games in which players move sequentially rather than simultaneously
- Because the payoff each achieves still depends on the other’s decision, the player who moves first must anticipate the decision the next player will make in response
Decisions can be diagrammed as the nodes in a decision tree, which branch off into the choices or payoffs that follow from each option
Backward induction can be used to analyze decision tree and determine the best course of action at each stage of the game

In a game with first-mover advantage, the player who moves first gets a higher payoff than those who follow
Example: a one-round bargaining game in which the person who makes the first offer gets virtually everything
The ability to bargain over multiple rounds of offers and counter-offers dilutes the first-mover advantage

The ability to make counter-offers transforms bargaining from a game in which first-mover advantage trumps everything into a game of patience
Bargaining takes time
- In every round of bargaining that takes place before the players reach agreement, the value of the payoff they are splitting goes down
The more patient player who places more value on money in the future relative to money in the present, has an advantage
The surplus will be divided in proportion to the patience of each player

In a sequential game, limiting your own choices can change your opponent’s behaviour
Example: following a commitment strategy turns a non-credible threat into a credible one, changing the payoffs associated with an opponent’s options