Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I even say who wrote them. If you have more recent summaries to add to this collection, send them my way I guess. Sorry for the ads; they cover the costs of keeping this online.
McCarty and Groseclose. 2000. The politics of blame: Bargaining before an audience. AJPS.
Most models of Congressional-presidential bargaining are two-player games--but in reality, both sides are playing before a third player, the electorate, and both sides have incentives to behave differently as a result. Under divided government in particular, Congress wants to pass things that it knows the president will veto (to make him look extreme), and the president might sign things that are worse (for his preferences) than the status quo, but which help him appear moderate.
Though Congress and the president may (or may not, but that's irrelevant) have perfect information about one another's preferences, vetoes and gridlock can happen anyway. The electorate lacks information about the president's (and maybe Congress's ?) preferences, so politicians want to send the public incentives to signal these preferences (for electoral reasons). Thus, Congress and the president might play the "blame game": Congress will pass a bill that it knows the president will veto, or the president will sign a bill that gives more than he wants to to Congress. "Thus, despite Congress and the president being completely informed, an uninformed thir party causes the outcome to be Pareto inefficient."
It might be good to keep committee hearings, labor-management disputes, and other negotiations secret. Without an audience, the parties will bargain for a mutually acceptable deal. But with an audience, the parties have incentives to send signals to the audience--which might inhibit making any agreement.
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