Non-linear strategies in a linear quadratic differential game

We study non-linear Markov perfect equilibria in a two agent linear quadratic differential game. In contrast to the literature owing to Tsutsui and Mino (1990), we do not associate endogenous subsets of the state space with candidate solutions. Instead, we address the problem of unbounded-below value functions over infinite horizons by use of the `catching up optimality' criterion. We present sufficiency conditions for existence based on results in Dockner, Jorgenson, Long and Sorger (2000). Applying these to our model yields the familiar linear solution as well as a condition under which a continuum of non-linear solutions exist. As this condition is relaxed when agents are more patient, and allows more efficient steady states, it resembles a Folk Theorem for differential games. The model presented here is one of atmospheric pollution; the results apply to differential games more generally.differential game, non-linear strategies, catching up optimal, Folk Theorem

Formal representation and proof for cooperative games

In this contribution we present some work we have been doing in representing and proving theorems from the area of economics, and mainly we present work we will do in a project in which we will apply mechanised theorem proving tools to a class of economic problems for which very few general tools currently exist. For mechanised theorem proving, the research introduces the field to a new application domain with a large user base; more specifically, the researchers are collaborating with developers working on state-of-the-art theorem provers. For economics, the research will provide tools for handling a hard class of problems; more generally, as the first application of mechanised theorem proving to centrally involve economic theorists, it aims to properly introduce mechanised theorem proving techniques to the discipline.\u

The ForMaRE Project - Formal Mathematical Reasoning in Economics

The ForMaRE project applies formal mathematical reasoning to economics. We seek to increase confidence in economics' theoretical results, to aid in discovering new results, and to foster interest in formal methods, i.e. computer-aided reasoning, within economics. To formal methods, we seek to contribute user experience feedback from new audiences, as well as new challenge problems. In the first project year, we continued earlier game theory studies but then focused on auctions, where we are building a toolbox of formalisations, and have started to study matching and financial risk. In parallel to conducting research that connects economics and formal methods, we organise events and provide infrastructure to connect both communities, from fostering mutual awareness to targeted matchmaking. These efforts extend beyond economics, towards generally enabling domain experts to use mechanised reasoning.Comment: Conference on Intelligent Computer Mathematics, 8--12 July, Bath, UK. Published as number 7961 in Lecture Notes in Artificial Intelligence, Springe

Budget Imbalance Criteria for Auctions: A Formalized Theorem

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such a sum is not constant. In particular, this theorem applies to the important case of a second-price Vickrey auction, where it reduces to a basic result of which a novel proof is given. To enhance the confidence in this new theorem, it has been formalized in Isabelle/HOL: the main results and definitions of the formal proof are re- produced here in common mathematical language, and are accompanied by an informal discussion about the underlying ideas.Comment: 6th Podlasie Conference on Mathematics 2014, 11 page

Optimal two stage committee voting rules

We study option management by committee. Analysis is illustrated by tenure decisions. Our innovations are two-fold: we treat the committee's problem as one of social choice, not of information aggregation; and we endogenise the outside option: rejecting a candidate at either the probationary or tenure stage return the committee to a candidate pool. For committees with N members, we find three key results: (1) a candidate's fate depends only on the behaviour of two `weather-vane' committee members - generalised median voters; (2) enthusiastic assessments by one of these weather-vanes may harm a candidate's chances by increasing others' thresholds for hiring him; and (3) sunk time costs may lead voters who opposed hiring a candidate to favour tenuring him, even after a poor probationary performance. We also characterise the optimal voting rule when N=2. A patient or perceptive committee does best with a (weak) majority at the hiring stage and unanimity at the tenure stage. An impatient or imperceptive committee does best under a double (weak) majority rule. If particularly impatient or imperceptive, this rule implies that any hire is automatically tenured. Perversely, the performance of a patient, imperceptive committee improves as its perceptiveness further declines.intertemporal strategic voting, real options, social choice, heterogenous priors, tenure

The commons with capital markets

We explore commons problems when agents have access to capital markets. The commons has a high intrinsic rate of return but its fruits cannot be secured by individual agents. Resources transferred to the capital market earn lower returns, but are secure. In a two period model, we assess the consequences of market access for the commons' survival and welfare; we compare strategic and competitive equilibria. Market access generally speeds extinction, with negative welfare consequences. Against this, it allows intertemporal smoothing, a positive effect. In societies in which the former effect dominates, market liberalisation may be harmful. We reproduce the multiple equilibria found in other models of competitive agents; when agents are strategic, extinction dates are unique. Strategic agents generally earn their surplus by delaying the commons' extinction; in unusual cases, strategic agents behave as competitive ones even when their numbers are small.commons, capital markets, Washington Consensus, property rights

The Road to Extinction: Commons with Capital Markets

We study extinction in a commons problem in which agents have access to capital markets. When the commons grows more quickly than the interest rate, multiple equilibria are found for intermediate commons endowments. In one of these, extinction is hastened and welfare decreases in the endowment, a resource curse. An extraction tax reduces welfare in this 'cursed' equilibrium, increases it in the other equilibrium in which the commons is eventually depleted, and expands the set of commons stocks that are never depleted. Capital market access harms societies with low commons endowments. In the limit, as marginal extraction costs become constant, `jump extinctions' occur. Finally, when the commons grows less quickly than the interest rate, there is a unique extinction date for each endowment level.commons, capital markets, extinction, resource curse, storage, multiple equilibria, rational expectations equilibrium

The road to extinction: commons with capital markets

Competitive agents extract in continuous time from a commons. Capital market access allows them to both save and borrow against their extraction stream. When the commons asset grows more quickly than the privately stored one, multiple equilibria are found for intermediate commons endowments. One of these has the extinction date and welfare decrease in the endowment, a resource curse. When the commons asset grows less quickly than the privately stored one, there is a unique extinction date for each endowment level. In the limit, as marginal extraction costs become constant, `jump extinctions' occur. In cases with multiple equilibria: welfare is increased for low initial stock levels when agents do not have access to capital markets, but decreased otherwise; and an extraction tax reduces welfare in the `cursed' equilibrium, increases it in the other finite extinction equilibrium and expands the set of commons stocks that are never extinguishedcommons, capital markets, extinction, resource curse, storage, multiple equilibrium, rational expectations equilibrium

Neural regulation of cancer: from mechanobiology to inflammation.

Despite recent progress in cancer research, the exact nature of malignant transformation and its progression is still not fully understood. Particularly metastasis, which accounts for most cancer death, is a very complex process, and new treatment strategies require a more comprehensive understanding of underlying regulatory mechanisms. Recently, the sympathetic nervous system (SNS) has been implicated in cancer progression and beta-blockers have been identified as a novel strategy to limit metastasis. This review discusses evidence that SNS signaling regulates metastasis by modulating the physical characteristics of tumor cells, tumor-associated immune cells and the extracellular matrix (ECM). Altered mechanotype is an emerging hallmark of cancer cells that is linked to invasive phenotype and treatment resistance. Mechanotype also influences crosstalk between tumor cells and their environment, and may thus have a critical role in cancer progression. First, we discuss how neural signaling regulates metastasis and how SNS signaling regulates both biochemical and mechanical properties of tumor cells, immune cells and the ECM. We then review our current knowledge of the mechanobiology of cancer with a focus on metastasis. Next, we discuss links between SNS activity and tumor-associated inflammation, the mechanical properties of immune cells, and how the physical properties of the ECM regulate cancer and metastasis. Finally, we discuss the potential for clinical translation of our knowledge of cancer mechanobiology to improve diagnosis and treatment