Index
2 × 2 bimatrix games
3 × 3 symmetric game
Aj and iA
E(X, Y)
E(X, j)=X Aj
E(i, Y)=iA· YT
–core
3 player cooperative games
exact formulas
additive game
allocation
definition
allocation of taxes
asymptotic stability
auctions
application to Bertrand model
complete information
definitions
Dutch
English
English and Dutch
Nash equilibrium
first-price sealed-bid
optimal bidding
general bidding function
need for a reserve price
need for middleman
optimal buy-it-now price
private value
reserve price
revenue equivalence theorem
symmetric, private value
take-it-or-leave-it rule
variance of selling price
Banzhaf-Coleman index
bargaining
feasible set
KS solution
Nash axioms
Nash’s theorem
safety, security, status quo point
the nonlinear program
threat security point
threat strategies
baseball game
battle of the sexes game
Bayesian game
Beer or Quiche
Bertrand model of production
best response
and ESS
Stackelberg game
best response set
and rational reaction set
definition
best response strategy
best threat strategies
bimatrix
Braess’s paradox
buy-it-now price
calculus
and interior saddles
calculus method
and the equations for Nash equilibrium
finding interior Nash points
finding interior saddle points
carriers of a game
cat versus rat game
characteristic function
(0, 1) normalization
bimatrix games
definition
from nonzero sum game
general formula from nonzero sum
scheduling problem
superadditivity
coalitions
Colonel Blotto game
completely mixed games
completely mixed strategy
concave
constant sum games
continuous game
convex function
convex hull
convex set
cooperative game
conversion to normalized
group rationality
individual rationality
cooperative games
cost allocation
core of a cooperative game
as set of undominated imputations
condition to be nonempty, three-person game
definition
may be empty
subset of the reasonable set
correlated equilibrium
existence
linear program
Cournot duopoly model
uncertain costs
definition of Aj, iA
deviant strategy
division of land game
dominance
dominance by a convex combination
dominance through a convex combination
dominated by a convex combination
dominated imputations
dominated strategy
definition
dual linear program
dual program
duality theorem
duels
continuum strategies
general accuracy functions
Hamilton-Burr
noisy
nonsymmetric
silent
dummy player
Dutch auction
economic entry deterrence
endgame in poker
English auction
English auction game
equality of payoffs
equality of payoffs theorem
equilibrium solution
equilibrium theorem
ESS
asymptotic stability
ESS is a Nash equilibrium
essential game
evolution of money
evolutionary stable strategy
definition
equivalent definition
evolutionary stable strategy (ESS)
excess function
definition
dissatisfaction
expected fitness
expected payoff
expected value of a random variable
extensive form
extensive games
backward induction
decision nodes
Gale’s roulette
Gambit
information set
information sets
node
node value
perfect information
perfect recall
sequential moves
simultaneous moves
Solomon’s decision
subgame perfect equilibrium
extreme points
feasible set
first-price sealed-bid auction
fitness
fixed-point theorem
frequencies
frequency dynamics
Gambit
game matrix
game of chicken
game with invertible matrix
games
and asymptotic stability
and evolution of currency
and evolutionary stable strategies
bargaining with safety point
battle of sexes
characteristic function game
characterization of value and saddle
chicken
completely mixed
cooperative solution
core of
debtor’s problem
entry deterrence
equality of payoffs theorem
evens or odds
expected payoff
extensive form
fair allocation of taxes
formulas for 2 × 2 games
invertible matrix
KS solution
mixed strategy
Nash’s bargaining theorem
nucleolus
Pascal’s theology game
safety value for nonzero sum
Shapley value
symmetric
symmetric bimatrix
the arms race
threat strategies
three hospitals
United Nations
upper and lower value
verifcation tool
welfare problem
garbage game
grand coalition
graphical method
graphical method for 2 × m and n × 2
group rationality
Hamilton-Burr duel
hawk–dove game
Hessian matrix
imputations
and inessential games
and the core
and the least core
definition
fair allocation
reasonable allocation set
relation with normalized game
set of
individually rational
inessential game
additive characteristic function
inessential game
information sets
interior critical point
interior Nash equilibria
interior Nash equilibrium
invertible matrix game
invertible matrix games
Maple commands
invertible matrix theorem for nonzero sum games
John Nash
Kakutani’s fixed point theorem
Kalai and Smorodinsky
Kalai–Smorodinsky bargaining solution
KS line
least core
Lemke and Howson
Lemke-Howson algorithm
linear program
check for empty core
constraint set
direct method for games
direct method for player I
direct method for player II
dual problem
duality theorem
empty core
first method for matrix games
for player I
for player II
least core
primal problem
simplex method step by step
standard form
transformation of game to standard form
linear programming
linear programs
simplex method
losing coalition
lower value
lower value of the game
Maple commands
accuracy functions in duels
animation of -core
bargaining graph
bargaining solution
binomial coefficient
calculation of least core
calculation of the nucleolus
demand and cost functions
empty core
evolutionary stable strategy
for Nash equilibria
game with invertible matrix
graph of least core
interior Nash point
linear program solution
linear programming method
Maple procedure
nonlinear program for bargaining
nonlinear program for rich and poor game
phase portrait
plot of feasible set in bargaining
plot of instability
plot of payoff pairs
set a reserve price
solution of a linear system
solve a linear program for player I
solve a linear program for player II
solve an ode
stability and instability
upper and lower values
matrix games
linear programming
maxmin strategy
maxmin strategy for player I
maxmin strategy for player II
middleman
mixed strategies
expected payoff E(X, Y)
mixed strategies for continuous games
mixed strategy
Nash equilibrium
and auctions
and evolutionary stable strategies
and safety levels
and the traveler’s paradox
choosing by risk-dominance
choosing by uninvadability
choosing using stability
conditions for general bimatrix games
Cournot duopoly
general demand and cost
definition for bimatrix games
equality of payoffs
existence for continuous strategies
finding interior by calculus
general definition for N players
inequalities for 2 × 2 bimatrix games
median voter model
mutual best response
nonexistence in Bertrand model
nonlinear program solution
payoff-dominant
proof of existence bimatrix games
pure strategies
self-enforcing
test for pure strategies
Nim
noisy duel
nonlinear program
nonlinear programming problem
nonsymmetric duel
nucleolus
algorithm
comparison with Shapley vector
exact formulas for empty core
exact formulas for nonempty core
Maple examples
Mathematica code
sequence of linear programs
solution using maple
theorem
optimal bidding function in a Dutch auction
optimal threat security point
optimal threat strategies
Pareto-optimal
Pareto-optimal boundary
Pareto-optimal boundary of the feasible set
Pareto-optimality
payoff vector
definition
payoff-dominant
payoff-dominant Nash equilibrium
payoffs
player I’s linear program
player II’s linear program
primal program
prisoner’s dilemma
properties of optimal strategies
pure strategies
random contest
rational reaction set
rational reaction sets
reasonable set
replicator dynamics
generic case
two pure strategies
reserve price
risk-dominance
rock-paper-scissors
Russian Roulette game
saddle point
saddle point in mixed strategies
saddle point in pure strategies
saddle point of f(x, y)
saddle point theorem in calculus
safety level
safety point
safety value of a game
scheduling problem
security point
sequential bargaining
set of mixed strategies Sk
Shapley value
allocation
allocation table
Shapley Value Maple
Shapley–Shubik index
silent duel
asymmetric, discrete
continuous mixed strategy
continuum of strategies
discrete
simple cooperative game
simple game
simplex method
worked example
skew symmetric
slack variables
social optimum
social welfare
solve a bimatrix game
solve the linear programs using Maple
solving matrix games algebraically
stability
and ESS
and Nash equilibria
definition
stability theorem
system of two equations
Stackelberg economic model
stag–hare game
stationary solution
status quo
status quo point
steady state
steady-state solution
strategic equivalence
strategies
strict Nash is ESS
subgame perfect equilibrium
submarine game
superadditivity
symmetric games
symmetric two-person bimatrix game
take-it-or-leave-it price
target problem
tragedy of commons
trajectory
traveler’s paradox
two period consumption
two thirds of the average
two-person zero sum game
uninvadable
uninvadable strategy
upper value
upper value of the game
value
zero sum matrix game
von Neumann
and existence of saddle point
minimax theorem
proof of minimax theorem
short biography
war of attrition
welfare game
winning coalition
zero sum equilibrium
zero sum game