Game Theory with Applications to Finance and Marketing

Although making arrangements with a third party is not credible whena player can renegotiate those arrangements with the third party withoutbeing seen by the rival, committing with the rival directly is credible.(Think of deposits.) By committing with the rival, re-negotiationof the commitment will be detected directly, and there is actually noroom for such re-negotiation. Since we have assumed that contractingis feasible (or else how did player 1 commit with the third party inthe above scenario?), we can allow the two firms to write a bindingcontract, saying that a player that is found to have played “Confess”ex-post will be liable to paying the rival 2 (units of utility). To implementthe contract, one player can draw it, and write explicitly that thecontract is valid if and only if it has both players’ signatures on it. Itis easy to see that with this explicit statement both players will sign it,and given it, both players are better off. 27In decision theory, a single decision maker’s welfare always increaseswhen the feasible set of choices is enlarged. The non-cooperative gametheory essentially treats multiple decision makers’ decision-making problems.The example we present here shows that, with multiple decisionmakers, enlarging their strategy spaces need not raise their welfare;they may become worse off actually.With a single decision maker, he is always better off with more infor-Simply because 3 8 rather than 1 2 is the best response for firm 1 against firm 2’s quantity 1 4 .However, in this case, rationally expecting this, firm 2 will not take q1 ∗ = 1 2as “given” anymore! This example shows that commitment power (the capability of making “convincingcommitments”) is a reason why firm 1 instead of firm 2 can get to be the “leader” of theStackelberg game; being a leader, the firm must be able to commit its move and convinceits rival that it will not be able to “reverse” the committed action afterwards. If firm 1has the commitment power, while firm 2 does not have it, then firm 1 gets to be the leaderof the game.27 In reality, explicit binding contracts may not be feasible, since the two players maybe considered collusive, which is illegal and detrimental to other people’s welfare; imaginethat two players are the two firms in the preceding game of market share competition. In asubsequent Lecture on repeated games, we shall demonstrate the possibility of sustaining acommitment between two self-interested players by allowing the latter to tacitly coordinatetheir intertemporal strategies. The basic idea is that relationship has value: with a longtermrelationship, a short-term move against the two-players’ common interest will beretaliated in the future, and this threat helps the players attain Pareto improved outcomeseven if signing binding contracts is not feasible.45