Consider the following game. you pay me an entry fee of x dollars, then i roll a fair die. if the die shows a number less than 3, i pay you nothing; if the die shows a 3 or 4, i give you back your entry fee of x dollars; if the die shows a 5, i will pay you $1; and if the die shows a 6, i pay you $3. what value of x makes the game fair (in terms of expected value) for both of us

Why is the cournot equilibrium an​ equilibrium? a. there are​ short-run barriers to exit in a cournot​ duopoly, so both firms cannot alter their output levels. b. given the other​ firm's level of​ production, both firms are maximizing profits and cannot improve their situation by unilaterally altering their level of output. c. both firms operate at zero profit under a cournot​ equilibrium, so they would face negative profits if they change output. d. both firms operate at minimum​ long-run average cost under a cournot​ equilibrium, so changes to output would reduce​ long-run profits. even if they​ can't collude, why​ don't firms set their outputs at the joint​ profit-maximizing levels​ (i.e., the levels they would have chosen had they​ colluded)? a. given that other firm produces at the collusive​ level, a firm could increase their own profits by increasing output above the collusive level. b. the midpoint of the collusion curve​ (i.e., the collusive​ outcome) lies below the reaction​ curves, so both firms have an incentive to increase output under the cournot duopoly. c. both a and b are correct d. both a and b are incorrect