Intellectual Property and the Prisoner’s Dilemma: A Game Theory Justification of Copyrights, Patents, and Trade Secrets

In this article, I will offer an argument for the protection of intellectual property based on individual self-interest and prudence. In large part, this argument will parallel considerations that arise in a prisoner’s dilemma game. In brief, allowing content to be unprotected in terms of free access leads to a sub-optimal outcome where creation and innovation are suppressed. Adopting the institutions of copyright, patent, and trade secret is one way to avoid these sub-optimal results

Beyond the Need to Boast: Cost Concealment Incentives and Exit in Cournot Duopoly

This paper studies the incentives for production cost disclosure in an asymmetric Cournot duopoly. Whereas the efficient firm (consumers) prefers information sharing (concealment) when the firms choose accommodating strategies in the product market, the firm (consumers) may prefer information concealment (sharing) when it can exclude its competitor from the market. Hence, the rankings of expected profit and consumer surplus can be reversed if exit of the inefficient firm is possible. Although the efficient firm has stronger incentives to share information when it shares strategically, there remain cases in which the firm conceals information in equilibrium to induce exit.cost asymmetry, Cournot duopoly, exit, information disclosure, precommitment

Lower Bounds on Implementing Robust and Resilient Mediators

We consider games that have (k,t)-robust equilibria when played with a mediator, where an equilibrium is (k,t)-robust if it tolerates deviations by coalitions of size up to k and deviations by up to $t$ players with unknown utilities. We prove lower bounds that match upper bounds on the ability to implement such mediators using cheap talk (that is, just allowing communication among the players). The bounds depend on (a) the relationship between k, t, and n, the total number of players in the system; (b) whether players know the exact utilities of other players; (c) whether there are broadcast channels or just point-to-point channels; (d) whether cryptography is available; and (e) whether the game has a $k+t)-punishment strategy; that is, a strategy that, if used by all but at most$k+t$ players, guarantees that every player gets a worse outcome than they do with the equilibrium strategy

Squares of matrix-product codes

The component-wise or Schur product $C*C'$ of two linear error-correcting codes $C$ and $C'$ over certain finite field is the linear code spanned by all component-wise products of a codeword in $C$ with a codeword in $C'$. When $C=C'$, we call the product the square of $C$ and denote it $C^{*2}$. Motivated by several applications of squares of linear codes in the area of cryptography, in this paper we study squares of so-called matrix-product codes, a general construction that allows to obtain new longer codes from several ``constituent'' codes. We show that in many cases we can relate the square of a matrix-product code to the squares and products of their constituent codes, which allow us to give bounds or even determine its minimum distance. We consider the well-known $(u,u+v)$-construction, or Plotkin sum (which is a special case of a matrix-product code) and determine which parameters we can obtain when the constituent codes are certain cyclic codes. In addition, we use the same techniques to study the squares of other matrix-product codes, for example when the defining matrix is Vandermonde (where the minimum distance is in a certain sense maximal with respect to matrix-product codes).This work is supported by the Danish Council for IndependentResearch: grant DFF-4002-00367, theSpanish Ministry of Economy/FEDER: grant RYC-2016-20208 (AEI/FSE/UE), the Spanish Ministry of Science/FEDER: grant PGC2018-096446-B-C21, and Junta de CyL (Spain): grant VA166G