Indivisibility, Fairness, Farsightedness and their Implications for Security

fair division, commitment, peace treaties, terrorist motivation

Resolving Social Issues in a Merger: A Fair-Division Approach

One of the most elusive ingredients in the success of a deal is what deal makers euphemistically refer to as "Social issues" - how power, position, and status will be allocated among the merging companies' executives. A failure to resolve these issues often leads to the destruction of shareholder wealth and portrayal of top executives as petty corporates chieftains, unable to subordinate their selfish interests to the goal of promoting shareholder well-being.MERGERS ; EFFICIENCY ; EQUITY

Technical Change and Industrial Dynamics as Evolutionary Processes

This work prepared for B. Hall and N. Rosenberg (eds.) Handbook of Innovation, Elsevier (2010), lays out the basic premises of this research and review and integrate much of what has been learned on the processes of technological evolution, their main features and their effects on the evolution of industries. First, we map and integrate the various pieces of evidence concerning the nature and structure of technological knowledge the sources of novel opportunities, the dynamics through which they are tapped and the revealed outcomes in terms of advances in production techniques and product characteristics. Explicit recognition of the evolutionary manners through which technological change proceed has also profound implications for the way economists theorize about and analyze a number of topics central to the discipline. One is the theory of the firm in industries where technological and organizational innovation is important. Indeed a large literature has grown up on this topic, addressing the nature of the technological and organizational capabilities which business firms embody and the ways they evolve over time. Another domain concerns the nature of competition in such industries, wherein innovation and diffusion affect growth and survival probabilities of heterogeneous firms, and, relatedly, the determinants of industrial structure. The processes of knowledge accumulation and diffusion involve winners and losers, changing distributions of competitive abilities across different firms, and, with that, changing industrial structures. Both the sector-specific characteristics of technologies and their degrees of maturity over their life cycles influence the patterns of industrial organization ? including of course size distributions, degrees of concentration, relative importance of incumbents and entrants, etc. This is the second set of topics which we address. Finally, in the conclusions, we briefly flag some fundamental aspects of economic growth and development as an innovation driven evolutionary process.Innovation, Technological paradigms, Technological regimes and trajectories, Evolution, Learning, Capability-based theories of the firm, Selection, Industrial dynamics, Emergent properties, Endogenous growth

Fair Resource Sharing with Externailities

We study a fair resource sharing problem, where a set of resources are to be shared among a set of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, whom they share the same resource with. Apparently, the strong notion of envy-freeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even to decide the existence of such a strongly envy-free assignment is an intractable problem. Thus, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envy-freeness, can be achieved: an agent i envies another agent j only when i envies both the resource and the mates of j. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dorm-mates. We show that when the capacity of the dorms is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment; nevertheless, the result fails to hold immediately when the capacities increase to 3, in which case even Pareto envy-freeness cannot be guaranteed. In addition to the existential results, we also investigate the implications of envy-freeness on proportionality in our model and show that envy-freeness in general implies approximations of proportionality

Algorithms for Competitive Division of Chores

We study the problem of allocating divisible bads (chores) among multiple agents with additive utilities, when money transfers are not allowed. The competitive rule is known to be the best mechanism for goods with additive utilities and was recently extended to chores by Bogomolnaia et al (2017). For both goods and chores, the rule produces Pareto optimal and envy-free allocations. In the case of goods, the outcome of the competitive rule can be easily computed. Competitive allocations solve the Eisenberg-Gale convex program; hence the outcome is unique and can be approximately found by standard gradient methods. An exact algorithm that runs in polynomial time in the number of agents and goods was given by Orlin. In the case of chores, the competitive rule does not solve any convex optimization problem; instead, competitive allocations correspond to local minima, local maxima, and saddle points of the Nash Social Welfare on the Pareto frontier of the set of feasible utilities. The rule becomes multivalued and none of the standard methods can be applied to compute its outcome. In this paper, we show that all the outcomes of the competitive rule for chores can be computed in strongly polynomial time if either the number of agents or the number of chores is fixed. The approach is based on a combination of three ideas: all consumption graphs of Pareto optimal allocations can be listed in polynomial time; for a given consumption graph, a candidate for a competitive allocation can be constructed via explicit formula; and a given allocation can be checked for being competitive using a maximum flow computation as in Devanur et al (2002). Our algorithm immediately gives an approximately-fair allocation of indivisible chores by the rounding technique of Barman and Krishnamurthy (2018).Comment: 38 pages, 4 figure