Consider the following \(3 \times 3\) game.

(a) Find all pure strategy equilibria of this game.

(b) The picture below shows, for this game, the mixed-strategy sets \(X\) and \(Y\) for players I and II, but not which set is \(X\) and which is \(Y\). It also shows their subdivisions into best-response regions, but without labels, which you are asked to provide. Explain which triangle is \(\mathrm{X}\) and which is \(\mathrm{Y}\).For the three corners marked by \(a,b, e\) and \(p, s, u\), respectively, indicate which pure strategy \((1,0,0),(0,1,0)\), or \((0,0,1)\) they represent, and mark the triangles with the correct labels (1),..., 6). Is this game degenerate

(c) Based on these labels, identify all equilibria of the game in mixed strategies (using the indicated nodes \

(a,b, c,d, e,f, g\) and \(p, q, r, s, t, u, v\) ).

(d) Show all Lemke-Howson paths for missing label 1, and how they connect the equilibria of the game.

Transcribed Image Text:

2 3 II 6 4 4 4 4 4 2 4 (5) 6 2 3 6 4 5 0 1 0 6 5