Markov bargaining games

I consider an alternating offer bargaining game which is played by a risk neutral buyer and seller, where the value of the good to be traded follows a Markov process. For these games the existence of a perfect equilibrium is proved and the set of equilibrium payoffs and strategies are characterised. The main results are (a) if the buyer is less patient than the seller, then there will be delays in the players reaching an agreement, the buyer is forced into a suboptimal consumption policy and the equilibrium is ex-ante inefficient, and (b) if the buyer is more patient than the seller, then there is a unique and efficient equilibrium where agreement is immediate

Bargaining and the timing of investment

The joint determination of the timing of investment and wage bargaining is modelled. Two cases are considered: (a) There is an alternating-offer bargaining game over binding wage contracts and production is possible only when agreement is reached. (b) There are no binding contracts so revenue is divided in period-by-period bargaining post-investment. Investment can occur earlier in case (b) than in case (a) and the equilibrium in case (b) can Pareto-dominate the equilibrium with binding contracts. These conclusions depend on players' discount factors

Reputation and perfection in repeated common interest games

We consider a wide class of repeated common interest games perturbed with one-sided incomplete information: one player (the informed player) might be a commitment type playing the Pareto dominant action. As discounting, which is assumed to be symmetric, and the prior probability of the commitment type go to zero, it is shown that the informed player can be held close to her minmax payoff even when perfection is imposed on the equilibrium

Reputation and commitment in two-person repeated games without discounting

Two-person repeated games with no discounting are considered where there is uncertainty about the type of the players. If there is a possibility that a player is an automaton committed to a particular pure or mixed stage-game action, then this provides a lower bound on the Nash equilibrium payoffs to a normal type of this player. The lower bound is the best available and is robust to the existence of other types. The results are extended to the case of two-sided uncertainty. This work extends Schmidt (1993) who analyzed the restricted class of conflicting interest games

Optimal complementary auctions

This paper considers the situation where two products are sold by the same seller, but to disjoint sets of potential buyers. Externalities may arise from each market outcome to the other. The paper examines the nature of the seller's optimal mechanism, and, for example in the case of positive externalities, it is shown that the allocation decision in either market depends on the highest types in both markets. The optimal mechanism can be implemented by an indirect mechanism that essentially charges winning bidders for the value of their externalities. The analysis is applied to the sale of public sector franchises including exploration and development rights for oil and gas tracts

Reputation and commitment in two-person repeated games

Game Theory;Repeated Games

Disappearing private reputations in long-run relationships

For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps et al. [Imperfect monitoring and impermanent reputations, Econometrica 72 (2004) 407–432] showed that an informed player facing short-lived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is long-lived and has private beliefs, so that the informed player's reputation is private. The rate at which reputations disappear is uniform across equilibria and reputations also disappear in sufficiently long discounted finitely repeated games

Reputation in perturbed repeated games

The paper analyzes reputation effects in perturbed repeated games with discounting. If there is some positive prior probability that one of the players is committed to play the same (pure) action in every period, then this provides a lower bound for her equilibrium playoff in all Nash equilibria. This bound is tight and independent of what other types have positive probability. It is generally lower than Fudenberg and Levine's bound for games with a long-run player facing a sequence of short-run opponents. The bound cannot be improved by considering types playing finitely complicated history-dependent commitment strategies

Common learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe