Experimental Design
We summarize the elements of the model needed to define the experimental design Two risk-neutral players play a two-stage game with prize V=1000. In Stage~1 they simultaneously submit demands; if compatible, the pie is split as demanded, otherwise the game proceeds to Stage~2, a conflict in which Player~1's effort cost is fixed at c_1=80 and Player~2 chooses between low (c_L=80) and high (c_H=180) effort. Winning probabilities for Player~1 are (p_W^L,p_W^H,p_S^L,p_S^H)=(1/2,9/20,7/8,3/4), where the W/S index denotes weak/strong Player~1 type and L/H denotes Player~2's effort. Player~1 is strong with prior probability \pi (only she observes her type). Three asymmetric-information environments are studied: 1) Bluffing PBE: symmetric demand menu {200,500,800} for both players, prior \pi=3/5.
2) Feigning PBE: asymmetric demand menus, Player~1 from {200,650,800} and Player~2 from {200,350,800}, with d^1_M=650 and d^2_M=350; prior \pi=3/5. 3) Feigning PBE under alternative prior: same demand menus and payoffs as (2) but with prior lowered to \pi=3/10. We implement a $3\times 2$ between-subjects design. The three asymmetric-information environments above are crossed with the presence/absence of one-way pre-play communication from Player~1 to Player~2, yielding six treatment cells.