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Game Theory: lecture of May 3, 2019: Solving exercises on Game Theory and Evolutionary Game Theory

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Game Theory: lecture of May 3, 2019: Solving exercises on Game Theory and Evolutionary Game

Theory

Chiara Mocenni

Course of Game Theory

(2)

NE of a 3 strategies game

Let a game with three strategies be defined by the parametric payoff matrix A, with a ≥ 0

A =

1 a 1

0 0 2

−1 3 0

(3)

NE of a 3 strategies game

e

1

is strict NE

x

1

= (

2a−3a−9

, −

a−93

, −

a+3a−9

) is mixed NE for 0 ≤ a <

32

x

2

= (0,

25

,

35

) is mixed NE for 0 ≤ a ≤

32

e

1

is ESS because it is strict NE x

1

is not ESS because of e

1

x

2

is ESS. Check by applying the definition

equilibrium condition x

2∗T

Ax

2

= y

T

Ax

2

, ∀y ∈ ∆, then

stability condition x

2∗T

Ay > y

T

Ay ∀y ∈ ∆, y 6= x

2

(4)

NE of a 3 strategies game

Let a game with three strategies be defined by the parametric payoff matrix A, with a ≥ 0

A =

0 1 3

−3 2 4

−3 + 2a 2 + a 4

Riferimenti

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