 Game change In many real life scenarios, players do not know the full game tree they are playing. Even if they did, it might change during play. Or, at least, players may attempt to change the game. A concrete example is provided by the game tree in  Section 4.1.1.  There, the inefficient Backward induction outcome \((1, 0)\) could be avoided by E promising not to go left. When made binding (for instance through imposing a fine) this announcement eliminates histories and, consequentially, a new backward Induction outcome of \((2,2)\) results. Hence, both players can be made better off by restricting the freedom of one. Game theory has sophisticated analyses of such scenarios, including an analysis of ‘cheap talk’ (Osborne &amp; Rubinstein 1994), asking when such announcements are credible. On the logical side, this suggests an analysis of signaling games (van Rooy 2004). We are not aware of any logical work done in this direction.