Download
1 / 17
170 likes | 285 Vues
This overview provides a comprehensive understanding of game theory, focusing on strategic interaction and player decision-making. It covers key concepts such as players, strategies, outcomes, and payoffs. The discussion includes normal and extensive form games, Nash equilibria, and examples like the Prisoner's Dilemma, Chicken game, and Stag Hunt. Also explored are concepts of credibility in threats during deterrence scenarios. This guide is essential for grasping the dynamics of strategic choices and their implications in various game frameworks.
E N D
Game Theory Formalizing Strategic Interaction
A. Assumptions • Background Assumptions • Rational choice: Connected and Transitive preferences between Outcomes • Strategic interaction: Each side affects the other • Key Elements • Players – Two or more • Strategies – The choices players have • Outcomes – The results of the players’ choices • Payoffs (Preferences) – How much each player values each Outcome
1. Solving a Normal/Strategic-Form Game Without Math • Nash Equilibrium Neither player could do any better by unilaterally changing its strategy choice • To Solve: Examine each cell to see if either player could do better by unilaterally choosing a different Strategy, given that its opponent does nothing different. Example:
Solving a Game Without Math c. Not every game has a Nash Equilibrium • Example:
Solving a Game Without Math d. Some games have multiple Nash Equilibria • Example:
C. Common Strategic-Form Games • Prisoners’ Dilemma • Both players end up worse, even though each plays rationally! • Reflects Snyder and Jervis “predation” argument
C. Common Normal/Strategic-Form Games • Chicken • Equilibria: Someone swerves – but who? • Used to model “going nuclear” – manipulating the threat of something both sides wish to avoid (i.e. conquest by external enemies). • “Tied Hands” strategy – throw away the steering wheel!
C. Common Strategic-Form Games • “Stag Hunt”, aka the Assurance Game, aka Mixed-Motive PD • Equilibria: depends on trust – Nobody wants to be the only one looking for a stag! • Used to model non-predatory security dilemma, driven by fear instead of aggression
D. Games in Extensive Form: The Tree • Extensive form adds information: • What is the order of moves? • What prior information does each player have when it makes its decision? • Elements • Nodes – Points at which a player faces a choice • Branches – Decision paths connecting a player’s choices to the outcomes • Information Sets – When a player doesn’t know which node it is at • Outcomes – Terminal nodes
3. Solving an Extensive Form Game • Subgame Perfect Equilibrium – Eliminates “non-credible” threats from consideration • Process = Backwards induction – “If they think that we think…”
Incumbent ( 0, m ) No enter ( d, d ) Accommodate Entrant Enter ( w, w ) Fight Profit Implications: m > d > w and m > d > 0 4. Example: Monopolist’s Paradox: The Threat
Incumbent ( 0, m ) No enter ( d, d ) Accommodate Entrant Enter ( w, w ) Fight Profit Implications: m > d > w and m > d > 0 4. Example: Monopolist’s Paradox: Threat Not Credible!
Incumbent ( 0, m ) No enter ( d, d ) Accommodate Entrant Enter ( w, w ) Fight Profit Implications: m > d > w and m > d > 0 4. Example: Monopolist’s Paradox: The Equilibrium Subgame Perfect Equilibrium
E. Games of Deterrence: Credible Threat and Restraint War Preferences A: CapB SQ War FSB B: SQ FSB War CapB Nuke Attack Don’t Nuke CapB FSB Don’t Attack Nuke Subgame Perfect Equilibrium Don’t Nuke SQ Deterrence Success!!!
Preferences A: CapB SQ War FSB B:FSB SQ War CapB E. Games of Deterrence: Credible Threat But No Restraint War Nuke Subgame Perfect Equilibrium Attack Don’t Nuke CapB FSB Don’t Attack Nuke Don’t Nuke SQ Deterrence Fails!!!
Preferences A: CapB SQ War FSB B: SQ FSB CapB War E. Games of Deterrence: Restraint, But No Credible Threat War Nuke Attack Don’t Nuke CapB Subgame Perfect Equilibrium FSB Don’t Attack Nuke Don’t Nuke SQ Deterrence Fails!!!
