As early as the 1820s, the custom of pairing off had developed in Congress. If a member of Congress was to miss a formal vote, he would arrange beforehand with a member on the opposing side of the issue for the two not to vote. In modeling this situation, consider two members of Congress Representatives Smith and Joneswho, on a regular basis, would like to miss a House vote in order to take care of other business. Representative Smith would prefer to be away every three periods, starting with period 1 (hence periods 1, 4, 7, . . .), and receives a value of 3 from being away. Representative Jones would prefer to be away every three periods, starting with period 2 (hence, periods 2, 5, 8, . . .), and also receives value of 3. Call these periods the representatives traveling periods. In each such period, there is a House vote, and Smith receives a value of 5 from being in attendance and voting and a value of -5 if Jones is in attendance and votes. Analogously, Jones earns 5 from being in attendance and voting and -5 if Smith is in attendance and votes. Thus, if both are in attendance and vote, then Smith and Jones each have a payoff of 0 =(5 - 5). During a traveling period, a representatives payoff is 1) 3 if he is not in attendance and the other representative does not vote; 2) -2 (= 3 - 5) if he is not in attendance and the other representative votes; 3) 0 if both are in attendance and vote; and 4) 5 if he is in attendance and votes and the other does not vote. During a nontraveling period, a representatives payoff is 1) 0 if he is not in attendance and the other representative does not vote; 2) -5 if he is not in attendance and the other representative votes; 3) 0 if both are in attendance and vote; and 4) 5 if he is in attendance and votes and the other does not vote. In each period, the representatives simultaneously decide whether to be in attendance and vote. Each seeks to maximize the present value of his single-period payoff stream, where the discount factor is d. Find an SPNE in which each is not in attendance during his traveling periods and during those periods they pair off.