Bartering integer commodities with exogenous prices

The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This research report provides a mathematical and computational details associated to the mathematical programming based approaches proposed by Nasini et al. (accepted 2014) to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analyzed processes in the context of computational economics is provided, along with a Java implementation of the approaches described in this research report.Comment: 30 pages, 5 sections, 10 figures, 3 table

Socially Optimal Mining Pools

Mining for Bitcoins is a high-risk high-reward activity. Miners, seeking to reduce their variance and earn steadier rewards, collaborate in pooling strategies where they jointly mine for Bitcoins. Whenever some pool participant is successful, the earned rewards are appropriately split among all pool participants. Currently a dozen of different pooling strategies (i.e., methods for distributing the rewards) are in use for Bitcoin mining. We here propose a formal model of utility and social welfare for Bitcoin mining (and analogous mining systems) based on the theory of discounted expected utility, and next study pooling strategies that maximize the social welfare of miners. Our main result shows that one of the pooling strategies actually employed in practice--the so-called geometric pay pool--achieves the optimal steady-state utility for miners when its parameters are set appropriately. Our results apply not only to Bitcoin mining pools, but any other form of pooled mining or crowdsourcing computations where the participants engage in repeated random trials towards a common goal, and where "partial" solutions can be efficiently verified

Optimal production of transplant care services.

Most organ transplants are from dead donors. National transplant organizations exhibit considerable differences in terms of their donor population rates. Spain’s organization is by far the most efficient in this respect. We argue that much of the productivity advantage of Spain’s transplant organization proceeds from an efficient organization of the production chain, from organ procurement to transplantation. Transplant inputs from dead donors are analogous to a common resource for the transplant community. Their circulation through the national transplant organization creates public good externalities between the care units in charge of organ extraction and those in charge of transplantation. It is shown that a socially efficient production of transplant services requires an optimal control of both the production and the circulation of transplant inputs by the institutions of the transplant system.organ transplants; donation; public goods; production organization.

Asymmetric-valued Spectrum Auction and Competition in Wireless Broadband Services

We study bidding and pricing competition between two spiteful mobile network operators (MNOs) with considering their existing spectrum holdings. Given asymmetric-valued spectrum blocks are auctioned off to them via a first-price sealed-bid auction, we investigate the interactions between two spiteful MNOs and users as a three-stage dynamic game and characterize the dynamic game's equilibria. We show an asymmetric pricing structure and different market share between two spiteful MNOs. Perhaps counter-intuitively, our results show that the MNO who acquires the less-valued spectrum block always lowers his service price despite providing double-speed LTE service to users. We also show that the MNO who acquires the high-valued spectrum block, despite charing a higher price, still achieves more market share than the other MNO. We further show that the competition between two MNOs leads to some loss of their revenues. By investigating a cross-over point at which the MNOs' profits are switched, it serves as the benchmark of practical auction designs

The Rationality of Faith

According to Franklin (1998, 109) Pascal"s (1952) wager\ud and Leibniz"s theory that this is the best of all possible\ud worlds are latecomers in the Faith-and-Reason tradition.\ud Yet they have remained interlopers; for they have never\ud been taken as seriously as the older arguments for the\ud existence of God and other themes related to faith and\ud reason. Yet Pascal"s wager is of interest for historians of\ud probability and decision theorists for its first instance of\ud explicitly decision theoretic reasoning in print and its\ud invocation of infinite utility. Moreover, it is of interest for\ud psychologists for its discussion of voluntarism and for\ud philosophers of religion and theologians as a putative\ud proof that belief in God is an obligation of rationality (Hajek\ud 2000, 1). Furthermore, as decision theory and the mathematics\ud of infinities are flourishing and have advanced\ud rapidly over the last couple of years (McClennen 1994,\ud 115; Sobel 1996, 23; Vallentyne 2000) and as belief in\ud God has grown over the last terrorist attacks and religions\ud have multiplied over the last decades - just look at the new\ud world religion of the Bahai"s -, it might be worthwhile to\ud look at Pascal"s wager to get a new evaluation of the\ud situation