Nash Equilibrium and Weakly Dominated Actions Give an example of a two-player strategic game in which each player has finitely many actions and in the only Nash equilibrium both players' actions are weakly dominated. (Hint: you might need to go beyond 2-by-2 games.) -

Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land.                                                   Farmer 2   Farmer1                                                1 cow                  2+ cows                       1 cow                             8,8                    2,10                        2+cows                           10,2                     4,4   What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off)   The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…

Consider a beauty-contest game in which n players simultaneously pick a number between zero and 100 inclusive; the person whose number is closer to half of the average number wins a prize. What is the unique Nash equilibrium of this game? What number will a level-3 thinker pick?

The world has changed a bit. Microsoft and Google could still either cooperate or compete in the market for social media video software currently captured by Tik Tok, but their payoffs have changed. The table below shows their profits in billions of USD in each scenario. Use your mouse to point and click on the Nash equilibrium outcome(s). [There may be more than one so make sure you work out all the best response strategies]. Microsoft Cooperate 3,3 4,0 Cooperate O Don't cooperate O Google Don't cooperate O O 0,4 1,1