An Introduction to Game Theory


Martin J. Osborne

Table of Contents

1. introduction
    1.1 what is game theory?
        an outline of the history of game theory
        john von neumann
    1.2 the theory of rational choice
    1.3 coming attractions: interacting decision-makers
2. nash equilibrium: theory
    2.1 strategic games
    2.2 example: the prisoners dilemma
    2.3 example: back or stravinsky
    2.4 example: matching pennies
    2.5 example: stag hunt
    2.6 nash equilibrium:
        john f. nash jr.
        studying nash on the prisoners dilemma
    2.7 examples of nash equilibriu,
        experimental evidence on the prisoners dilemma
        focal points
    2.8 best response functions
    2.9 equilibrium in a single population: symmetric games and symmetric equilibria
3. nash equilibrium: illustrations
    3.1 cournots model of oligopoly
    3.2 bertrands model of oligopoly
        cournot, bertrand, and nash: some historical notes
    3.3 electoral competition
    3.4 war of attrition
    3.5 auctions
        auctions from babylonia to ebay
    3.6  accident law
4. mixed strategy equilibrium
    4.1 introduction
        some evidence on expected payoff functions
    4.2 strategic games in which players may randomize
    4.3 mixed strategy nash equilibrium
    4.4 dominated actions
    4.5 pure equilibria when randomization is allowed
    4.6 illusstration: expert diagnosis
    4.7 equilibrium in a single population
    4.8 illustration: reporting a crime
        reporting a crim: social psychology and game theory
    4.9 the formation of players beliefs
    4.10 extension: finding all mixed strategy nash equilibria
    4.11 extension: games in which each player has a continuum of actions
    4.12 appendix: representing preferences by expected payoffs
5. extensive games with perfect information: theory
    5.1 extensive games with perfect information
    5.2 strategies and outcomes
    5.3 nash equilibrium
    5.4 subgame perfect equilibrium
    5.5 finding subgame perfect equilibria of finite horizon games:
        backward induction
            ticktacktoe, chess, and related games
6. extensive games with perfect information: illustrations
    6.1 the ultimatum game, the holdup game, and agenda control
        experiments on the ultimatum game
    6.2 stackelbergs model of duopoly
    6.3 buying votes
    6.4 a race
7. extensive games with perfect information: extensions and discussions
    7.1 allowing for simultaneous moves
        more experimental evidence on subgame perfect equilibrium
    7.2 illustration: entry into a monopolized industry
    7.3 illustration: electoral competition with strategic voters
    7.4 illustration: committee decision-making
    7.5 illustration: exit from a declining industry
    7.6 allowing for exogenous uncertainty
    7.7 discussion: subgame perfect equilibrium and backward induction
8. coalitional game and the core
    8.1 coalitional games
    8.2 the core
    8.3 illustration: ownership and the distribution of wealth
    8.4 illustration: exchanging homogeneous horses
    8.5 illustration: exchanging homogenous houses
    8.6 illustration: voting
    8.7: illustration: matching
        matching doctors with hospitals
    8.8 discussion: other solution concepts
9. bayesian games
    9.1 motivational examples
    9.2 general definitions
    9.3 two examples concerning information
    9.4 illustration: cournots duopoly game with imperfect information
    9.5 illustration: providing a public good
    9.6 illustration: auctions
        auctions of the radio spectrum
    9.7 illustration: juries
    9.8 appendix: auctions with an arbitrary distribution of valuations
10. extensive games with imperfect information
    10.1 extensive games with imperfect information
    10.2 strategies
    10.3 nash equilibrium
    10.4 beliefs and equential equilibrium
    10.5 signalig games
    10.6 illustration: conspicuous expenditure as a signal of quality
    10.7 illustration: education as a signal of ability
    10.8 illustration: estrategic information transmission
    10.9 illustration: agenda control with imperfect information
11. strictly competitive games and maximinimization
    11.1 maxinimization
    11.2 maxinimization and nash equilibrium
    11.3 strictly competitive games
    11.4 maxminimzation and nash equilibrium in strictly competitive games
        maxminimization: some history
        empirical tests: experiments, tennis, and soccer
12. rationalizability
    12.1 rationalizability
    12.2 iterated elimination of strictly dominated actions
    12.3 iterated elimination of weakly dominated actions
    12.4 dominance solvability
13. evolutionary equilibrium
    13.1 monomorphic pure strategy equilibrium
        evolutionary game theory: some history
    13.2 mixed strategies and polymorphic equilibrium
    13.3 asymmetric contests
        side-blotched lizards
        explaining the outcomes of contests in nature
    13.4 variation on a theme: sibling behavior
    13.5 variation on a theme: the nesting behavior of wasps
    13.6 variation on a theme: the evolution of the sex ratio
14. repeated games: the prisoners dilemma
    14.1 the main idea
    14.2 preferences
    14.3 repeated games
    14.4 finitely repeated prisoners dilmemma
    14.5 infinitely repeated prisoners dilemaa
    14.6 strategies in an infentely repeated prisoners dilemma
    14.7 some nash equilibria of an infinitely repeated prisoners dilemma
    14.8 nash equilibrium payoffs of an infinitely repeated prisoners dilemma
        experimental evidence
    14.9 subgame perfect equilibria and the one-deviation property
        axelrods tournaments
    14.10 some subgame perfect equilibria of an infintely repeated prisoners dilemma
        reciprocal altruism among sticklebacks
    14.11 subgame perfect equilibrium payoffs of an infinitely repeated prisoners dilemma
        medival trade fairs
15. repeated games: general results
    15.1 nash equilibria of general infinitely repeated games
    15.2 subgame perfect equilibria of general infinitely repeated games
    15.3 finitely repeated games
    15.4 variation on a theme: imperfect observability
16. bargaining
    16.1 bargaining as an extensive game
    16.2 illustration: trade in a market
    16.3 nashs axiomatic model
    16.4 relation between strategic and axiomatic models
17. appendix mathematics
    17.1 numbers
    17.2 sets
    17.3 functions
    17.4 profiles
    17.5 sequences
    17.6 probability
    17.7 proofs