Unlike tic-tac-toe or checkers, in which optimal play leads to a draw, it is not known whether optimal play in chess ends in a win for White, a win for Black, or a draw. But after White moves first in chess, if Black has a double move followed by a double move of White and then alternating play, play is more balanced because White does not always tie or lead in moves. Symbolically, Balanced Alternation gives the following move sequence: After White's (W) initial move, first Black (B) and then White each have two moves in a row (BBWW), followed by the alternating sequence, beginning with W, which altogether can be written as WB/BW/WB/WB/WB… (the slashes separate alternating pairs of moves). Except for reversal of the 3rdand 4th moves from WB to BW (underscored), this is the standard chess sequence. Because Balanced Alternation lies between the standard sequence, which favors White, and a comparable sequence that favors Black, it is highly likely to produce a draw with optimal play, rendering chess fairer. This conclusion is supported by a computer analysis of chess openings and how they would play out under Balanced Alternation.

We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum—social welfare maximizing—allocations under the fairness notion of envy-freeness. Maxsum allocations can also be found under alternative notions such as equitability. In this paper, we examine the properties of these allocations. In particular, We provide conditions for when maxsum envy-free or equitable allocations are Pareto optimal and give examples where fairness with Pareto optimality is not possible. We also prove that maxsum envy-free allocations have weakly greater welfare than maxsum equitable allocations when agents have structured valuations, and we derive an approximate version of this inequality for general valuations.

A bargaining procedure, or mechanism, is a set of rules for two bargainers to follow as they make offers in order to reach a mutually satisfactory agreement on, say, a price. The efficiency of a mechanism is the expected surplus it delivers to the bargainers, relative to the surplus that a social planner would deliver, or that the bargainers themselves might achieve if they truthfully revealed their reservation prices. A theoretical limit on this efficiency is known, as is a specific procedure that achieves this maximum. But this procedure induces players to make offers that do not truly reflect their reservation prices. This paper discusses three procedures that induce honest offers, although they necessarily fail to achieve maximum efficiency. Each procedure has its own characteristics and costs, and each may have some uses in particular circumstances.

Players are assumed to rank each other as coalition partners. Two processes of coalition formation are defined and illustrated:•Fallback (FB): Players seek coalition partners by descending lower and lower in their preference rankings until some majority coalition, all of whose members consider each other mutually acceptable, forms.•Build-up (BU): Same descent as FB, except only majorities whose members rank each other highest form coalitions.BU coalitions are stable in the sense that no member would prefer to be in another coalition, whereas FB coalitions, whose members need not rank each other highest, may not be stable. BU coalitions are bimodally distributed in a random society, with peaks around simple majority and unanimity; the distributions of majorities in the US Supreme Court and in the US House of Representatives follow this pattern. Other examples of real-life coalition processes are discussed.