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Assume two countries, West and East, want to decide whether to abate (control) their pollution or not. For simplicity assume each country have only two strategies, abate or do not abate. The cost of abatement for these countries is given by CE = 5 + aE + aE2 CW = 2+aW +0.5 aW2 Where aE and aW present the abatement effort by country East and West respectively. If they put some effort on abatement, the quality of environment will improve for both countries. Assume the environmental benefits of abatement for each country is BE = 15 (aE + aW) BW = 25 (aE + aW) If both countries do nothing (no abatement) the estimated environmental damage for East is $5 billion and for West is $2 billion. a. Construct the normal form (table) game. b. Under which condition (abate, abate) is the unique Nash equilibrium for this game? c. find the abatement levels or (aE and aW) for both countries which satisfy the conditions you find in part b. Notes:aE and aW could be either 0 or any other amount which you may call it simply aE and aW. So, e.g., if country E doesn't abate aE=0, if it does it's abatement level is aE (which could be any positive number and then in the third part you will find a range of values which satisfies condition b). As a result, for cases that a country is abating, the net payoff will be a function of aE and/or aW.
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