Bitcoin's main innovation lies in allowing a decentralized system that relies on anonymous, profit driven miners who can freely join the system. We formalize these properties in three axioms: anonymity of miners, no incentives for miners to consolidate, and no incentive to assuming multiple...

A key part of decentralized consensus protocols is a procedure for random selection, which is the source of the majority of miners cost and wasteful energy consumption in Bitcoin. We provide a simple economic model for random selection mechanism and show that any PoW protocol with natural...

We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with...

We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. The set of outcomes that can arise in equilibrium for some information structure is equal to the...

This paper provides a dual characterization of the limit set of perfect public equilibrium payoffs in stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg, Levine and Maskin (1994), Kandori and Matsushima...

This paper characterizes an equilibrium payoff subset for Markovian games with private information as discounting vanishes. Monitoring is imperfect, transitions may depend on actions, types be correlated and values interdependent. The focus is on equilibria in which players report truthfully....

We analyze a class of games with interdependent values and linear best responses. The payoff uncertainty is described by a multivariate normal distribution that includes the pure common and pure private value environment as special cases. We characterize the set of joint distributions over...

We provide tight bounds on the rate of convergence of the equilibrium payoff sets for repeated games under both perfect and imperfect public monitoring. The distance between the equilibrium payoff set and its limit vanishes at rate (1 - delta)^{1/2} under perfect monitoring, and at rate (1 -...

This paper examines moral hazard in teams over time. Agents are collectively engaged in an uncertain project, and their individual efforts are unobserved. Free-riding leads not only to a reduction in effort, but also to procrastination. The collaboration dwindles over time, but never ceases as...