Mathematical framework for rigorous study of conflict and cooperation among rational, intelligent agents

Mathematical framework for rigorous study of conflict and cooperation among rational, intelligent agents

• Mathematical framework for rigorous study of conflict and cooperation among rational, intelligent agents

Two players simultaneously put down a coin, heads up or tails up.

• Two players simultaneously put down a coin, heads up or tails up.

• Two-Player zero-sum game

• N = {1, 2}; S1 = S2 = {H,T}

A profile of strategies is said to be

• A profile of strategies is said to be

• a pure strategy Nash Equilibrium if is a best

• response strategy against

No pure strategy NE here, only a mixed strategy NE

• No pure strategy NE here, only a mixed strategy NE

Every finite strategic form game has at least one mixed strategy Nash equilibrium

• Every finite strategic form game has at least one mixed strategy Nash equilibrium