Preface: This post represents a first, very rough approach to modeling "post-partisanship" as a governing strategy (as opposed to a campaign strategy, where it apparently can be effective, at least once). I presume the following definition of "post-partisanship:" consistent, good-faith efforts to effectuate superior public policies regardless of the political distribution of the gains and losses. I also presume (without any systematic evidence) that post-partisanship is possible. These presumptions may not hold in the real world, where "post-partisanship" tends to be ill-defined (if it is defined at all) and, depending on how it is defined, it may not even be possible. The model does not presume that President Obama (or anyone else) really is "post-partisan," however defined. Moreover, the model excludes a third important player, which is the president's own party in Congress. Including that third player would greatly complicate the model because the interests of presidential-party senators and representatives are not identical to those of the president. However, their existence explains why a president can sometimes accomplish his or her policy goals despite the opposition party's equilibrium strategy of total noncooperation.
A simple game-theoretic model suggests that post-partisanship cannot succeed as a governing (as opposed to campaign) strategy. As soon as a new president pledges to bridge the partisan divide, the strategy of the opposition becomes obvious: do not cooperate, at all. That opposition strategy effectively places the president in a no-win situation, in which he can really only minimize political costs. If the president maintains a post-partisan attitude, the opposition stands to gain extra concessions while the president appears weak and conciliatory. If the president, instead, deviates from his post-partisan stance, e.g., by playing tit-for-tat, his campaign promise is broken and he appears as a liar and a partisan. The only way a "post-partisan" president can succeed is if the opposition cooperates, which would (with rare exceptions*) be a strategic mistake. The payoff matrix for the game would look something like this:
The payoffs reflect expected political benefits or costs stemming from the combined behaviors of both players. In the top, left-hand quadrant, the president gains more than the opposition when both sides cooperate because it supports the president's claim of post-partisanship and shows it can be effective. The opposition stands to gain much more than the president, however, from non-cooperating, as indicated in the upper, right-hand quadrant, where the president's (presumed) efforts at post-partisanship result in greater concessions to the opposition, which creates the impression that the president is weak and overly conciliatory. If the president, instead, governs from a less compromising, uncooperative position, then his or her campaign promise of post-partisanship is exposed as a lie. In that case, even if the opposition cooperates, according to both bottom quadrants, the president suffers net political costs as an exposed partisan liar. To avoid those costs, the dominant strategy for the president is to cooperate. More importantly, the payoff matrix indicates that the president's precommitment to "post-partisanship" reduces his strategic options for negotiating. But for his or her precommitment to rise above the partisan fray, the president would have more strategic options for negotiating with the opposition, options that could, at least potentially, increase the total payoffs to cooperation relative to the payoffs for noncooperation.
If this model is basically correct, why would a president ever embrace post-partisanship as a governing strategy in the first place? Working backwards from the foreseeable payoffs, no president should adopt such an approach. This, however, is where the distinction, and the relationship, between post-partisanship as a governing strategy and post-partisanship as a campaign strategy becomes important. A candidate might understand very well that a governing strategy of post-partisanship is doomed to fail, and yet commit herself to post-partisanship as a campaign strategy, knowing that it can be effective (at least the first time around). Presidential candidates might be willing to accept the governing bind created by adopting the mantel of post-partisanship for the perceived boost in prospects for her initial election. After all, the campaign game is not the same as the governing game. Nevertheless, the analysis here suggests that the way the campaign game is played can affect the way the governing game is structured.
*One plausible exception to the opposition's general strategy of noncooperation would be in the unlikely event that the president embraced one of its own fundamental policy preferences (e.g., if Obama embraced tax cuts). In that case (and perhaps only that case), the net gains from cooperation might exceed the net gains from noncooperation.