Christian W. Bach

Pairwise epistemic conditions for Nash equilibrium

We introduce a framework for modeling pairwise interactive beliefs and provide an epistemic foundation for Nash equilibrium in terms of pairwise epistemic conditions locally imposed on only some pairs of players. Our main result considerably weakens not only the standard sufficient conditions by Aumann and Brandenburger (1995), but also the subsequent generalization by Barelli (2009). Surprisingly, our conditions do not require nor imply mutual belief in rationality.

Utility proportional beliefs

In game theory, basic solution concepts often conflict with experimental findings or intuitive reasoning. This fact is possibly due to the requirement that zero probability is assigned to irrational choices in these concepts. Here, we introduce the epistemic notion of common belief in utility proportional beliefs which also attributes positive probability to irrational choices, restricted however by the natural postulate that the probabilities should be proportional to the utilities the respective choices generate. Besides, we propose a procedural characterization of our epistemic concept. With regards to experimental findings common belief in utility proportional beliefs fares well in explaining observed behavior.

Agreeing to disagree with lexicographic prior beliefs

The robustness of Aumann’s seminal agreement theorem with respect to the common prior assumption is considered. More precisely, we show by means of an example that two Bayesian agents with almost identical prior beliefs can agree to completely disagree on their posterior beliefs. Besides, a more detailed agent model is introduced where posterior beliefs are formed on the basis of lexicographic prior beliefs. We then generalize Aumann’s agreement theorem to lexicographic prior beliefs and show that only a slight perturbation of the common lexicographic prior assumption at some–even arbitrarily deep–level is already compatible with common knowledge of completely opposed posterior beliefs. Hence, agents can actually agree to disagree even if there is only a slight deviation from the common prior assumption.

AGENT CONNECTEDNESS AND BACKWARD INDUCTION

We conceive of a player in dynamic games as a set of agents, which are assigned the distinct tasks of reasoning and node-specific choices. The notion of agent connectedness measuring the sequential stability of a player over time is then modeled in an extended type-based epistemic framework. Moreover, we provide an epistemic foundation for backward induction in terms of agent connectedness. Besides, it is argued that the epistemic independence assumption underlying backward induction is stronger than usually presumed.

The Effect of Payment Reversibility on E-commerce and Postal Quality

In this paper we develop a stylized model of competition between brick-and-mortar merchants and online retailers. An offline transaction, matching payment with delivery, is without risk for both the seller and the buyer. In an online transaction the seller faces the potential risk of non-payment while the buyer risks failed delivery. The effects of these two risks depend on the reversibility of payment. While traditional payment systems for e-commerce are reversible, virtual currencies like Bitcoin offer irreversible transactions. This shifts the risk from the receiver of the payment to its sender. The paper explores the effect of payment reversibility on competition between offline and online merchants and on the importance of postal quality for e-commerce. It finds that payment irreversibility may strengthen e-commerce due to reduced overall risk. Moreover, under reasonable conditions, postal operators have stronger incentives for quality since it affects volumes more strongly if payment is irreversible.

Blockchain Technology and Cryptocurrencies: Opportunities for Postal Financial Services

This paper explores opportunities arising from blockchain technology for postal operators. Blockchain technology has lately received a lot of interest by the media and the industry, especially in financial services. In the past years an entire ecosystem of new companies has developed, offering hundreds of different blockchain applications. Blockchains are a new kind of decentralized, secure and fast means of record-keeping. The first application of blockchain technology are cryptocurrencies like Bitcoin, which have become an alternative to commodity money and fiat money, but postal operators may be able to exploit this technology in a number of different ways.

Agreeing to disagree with limit knowledge

The possibility for agents to agree to disagree is considered in an extended epistemic-topological framework. In such an enriched context, Aumanns impossibility theorem is shown to no longer hold. More precisely, agents with a common prior belief satisfying limit knowledge instead of common knowledge of their posterior beliefs may actually entertain distinct posterior beliefs. Hence, agents can actually agree to disagree. In particular, agreeing to disagree with limit knowledge is illustrated within a representative epistemic-topological situation.