First, we check when it “pays to pay judgments,” that is, under what conditions a player will find it more profitable to pay any judgment rendered against him than to refuse to pay. (We ignore the sunk portion of the payoff which is unaffected by later behavior.) Paying the judgment J yields an additional payoff of - f ( J ) in the current period. In future periods, the player will spend Q to query the LM and earn a trading payoff of 1, for a total of 1 - Q. In terms of lifetime average payoff, paying the judgment leads to -(1 - S)f(J) + 6(1 - Q). If the trader refuses to pay the judgment, then his current period payoff is zero and, given the system, his payoff is also zero in every subsequent period. Therefore, it “pays to pay judgments” if and only if - (1 - 6)f(J) + 6( 1 - Q) 2 0, or equivalently,

DEFINE: Clarifies the compound condition for when a trader rationally opts to pay a judgment rather than face permanent exclusion from the market. Builds on: "A one-step deviation test verifies sequential equilibrium optimality."

PAUL R. MILGRO, PAUL R. MILGRO - THE ROLE O…, loc. 104