Game theoretical analysis of Kidney Exchange Programs

The goal of a kidney exchange program (KEP) is to maximize number of transplants within a pool of incompatible patient-donor pairs by exchanging donors. A KEP can be modelled as a maximum matching problem in a graph. A KEP between incompatible patient-donor from pools of several hospitals, regions or countries has the potential to increase the number of transplants. These entities aim is to maximize the transplant benefit for their patients, which can lead to strategic behaviours. Recently, this was formulated as a non-cooperative two-player game and the game solutions (equilibria) were characterized when the entities objective function is the number of their patients receiving a kidney. In this paper, we generalize these results for $N$-players and discuss the impact in the game solutions when transplant information quality is introduced. Furthermore, the game theory model is analyzed through computational experiments on instances generated through the Canada Kidney Paired Donation Program. These experiments highlighting the importance of using the concept of Nash equilibrium, as well as, the anticipation of the necessity to further research for supporting police makers once measures on transplant quality are available

One for all, all for one---von Neumann, Wald, Rawls, and Pareto

Applications of the maximin criterion extend beyond economics to statistics, computer science, politics, and operations research. However, the maximin criterion---be it von Neumann's, Wald's, or Rawls'---draws fierce criticism due to its extremely pessimistic stance. I propose a novel concept, dubbed the optimin criterion, which is based on (Pareto) optimizing the worst-case payoffs of tacit agreements. The optimin criterion generalizes and unifies results in various fields: It not only coincides with (i) Wald's statistical decision-making criterion when Nature is antagonistic, (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty, but it also generalizes (iii) Nash equilibrium in $n$-person constant-sum games, (iv) stable matchings in matching models, and (v) competitive equilibrium in the Arrow-Debreu economy. Moreover, every Nash equilibrium satisfies the optimin criterion in an auxiliary game

Self-enforcing Agreements on Water allocation

Many water allocation agreements in transboundary river basins are inherently unstable. Due to stochastic river flow, agreements may be broken in case of drought. The objective of this paper is to analyse whether water allocation agreements can be self-enforcing. An agreement is modelled as the outcome of bargaining game on river water allocation. Given this agreement, the bargaining game is followed by a repeated extensive-form game in which countries decide whether or not to comply with the agreement. I assess under what conditions such agreements are self-enforcing, given stochastic river flow. The results show that, for sufficiently low discounting, every efficient agreement can be sustained in subgame perfect equilibrium. Requiring renegotiation-proofness may shrink the set of possible agreements to a unique self-enforcing agreement. The solution induced by this particular agreement implements the “downstream incremental distribution”, an axiomatic solution to water allocation that assigns all gains from cooperation to downstream countries.Self-Enforcing Agreement, Repeated Extensive-Form Game, Water Allocation, Renegotiation-Proofness

Dynamic Decision Models for Managing the Major Complications of Diabetes

Diabetes is the sixth-leading cause of death and a major cause of cardiovascular and renal diseases in the U.S. In this dissertation, we consider the major complications of diabetes and develop dynamic decision models for two important timing problems: Transplantation in prearranged paired kidney exchanges (PKEs) and statin initiation. Transplantation is the most viable renal replacement therapy for end-stage renal disease (ESRD) patients, but there is a severe disparity between the demand and supply of kidneys for transplantation. PKE, a cross-exchange of kidneys between incompatible patient-donor pairs, overcomes many difficulties in matching patients with incompatible donors. In a typical PKE, transplantation surgeries take place simultaneously so that no donor may renege after her intended recipient receives the kidney. We consider two autonomous patients with probabilistically evolving health statuses in a PKE, and model their transplant timing decisions as a discrete-time non-zero-sum stochastic game. We explore necessary and sufficient conditions for patients' decisions to form a stationary-perfect equilibrium, and formulate a mixed-integer linear programming (MIP) representation of equilibrium constraints to characterize a socially optimal stationary-perfect equilibrium. We calibrate our model using large scale clinical data. We quantify the social welfare loss due to patient autonomy and demonstrate that the objective of maximizing the number of transplants may be undesirable. Patients with Type 2 diabetes have higher risk of heart attack and stroke, and if not treated these risks are confounded by lipid abnormalities. Statins can be used to treat such abnormalities, but their use may lead to adverse outcomes. We consider the question of when to initiate statin therapy for patients with Type 2 diabetes. We formulate a Markov decision process (MDP) to maximize the patient's quality-adjusted life years (QALYs) prior to the first heart attack or stroke. We derive sufficient conditions for the optimality of control-limit policies with respect to patient's lipid-ratio (LR) levels and age and parameterize our model using clinical data. We compute the optimal treatment policies and illustrate the importance of individualized treatment factors by comparing their performance to those of the guidelines in use in the U.S

A new model for coalition formation games

We present two broad categories of games, namely, group matching games and bottleneck routing games on grids. Borrowing ideas from coalition formation games, we introduce a new category of games which we call group matching games. We investigate how these games perform when agents are allowed to make selfish decisions that increase their individual payoffs versus when agents act towards the social benefit of the game as a whole. The Price of Anarchy (PoA) and Price of Stability (PoS) metrics are used to quantify these comparisons. We show that the PoA for a group matching game is at most kα and the PoS is at most k/α where k is the maximum size of a group and α is a switching cost. Furthermore we show that the PoA and PoS of the games do not change significantly even if we increase γ, the number of groups that an agent is allowed to join. We also consider routing games on grid network topologies. The social cost is the worst congestion in any of the network edges (bottleneck congestion). Each player\u27s objective is to find a path that minimizes the bottleneck congestion in its path. We show that the price of anarchy in bottleneck games in grids is proportional to the number of bends β that the paths are allowed to take in the grids\u27 space. We present games where the PoA is O(β). We also give a respective lower bound of Ω(β) which shows that our upper bound is within only a poly-log factor from the best achievable price of anarchy. A significant impact of our analysis is that there exist bottleneck routing games with small number of bends which give a poly-log approximation to the optimal coordinated solution that may use an arbitrary number of bends. To our knowledge, this is the first tight analysis of bottleneck games on grids

The effects of contract mechanisms between the government and private hospitals on the social utility

In this work, we deal with a real healthcare system, in which public and private hospitals with different characteristics co-exist. While public hospitals have lower costs, they also suffer from long waiting times, diminishing the perceived quality of care for patients. Conversely, private hospitals, with their higher fees, offer shorter waiting periods, resulting in a more favorable perception of quality. A balanced healthcare system could offer societal benefits. Pricing strategies greatly influence a patient's hospital selection. For instance, reduced fees in private hospitals attract more patients, consequently reducing overcrowding in public facilities and elevating the overall quality of services provided. This study aims to develop pricing models to foster a balanced and socially advantageous healthcare system. Within this system, private hospital pricing is determined through contract mechanisms with the government. Thus, we delve into the ramifications of various contract models between the government and private hospitals on social utility. Our findings underscore the communal advantages of contract mechanisms. Furthermore, we generalize the proposed models to be applicable to similar systems.info:eu-repo/semantics/publishedVersio

Incorporating Fairness Motives into the Impulse Balance Equilibrium and Quantal Response Equilibrium Concepts: An Application to 2x2 Games

Substantial evidence has accumulated in recent empirical works on the limited ability of the Nash equilibrium to rationalize observed behavior in many classes of games played by experimental subjects. This realization has led to several attempts aimed at finding tractable equilibrium concepts which perform better empirically; one such example is the impulse balance equilibrium (Selten, Chmura, 2008), which introduces a psychological reference point to which players compare the available payoff allocations. This paper is concerned with advancing two new, empirically sound, concepts: equity-driven impulse balance equilibrium (EIBE) and equity-driven quantal response equilibrium (EQRE): both introduce a distributive reference point to the corresponding established stationary concepts known as impulse balance equilibrium (IBE) and quantal response equilibrium (QRE). The explanatory power of the considered models leads to the following ranking, starting with the most successful in terms of fit to the experimental data: EQRE, IBE, EIBE, QRE and Nash equilibrium.Fairness, Inequity aversion, Aspiration level, Impulse balance, Quantal Response, Behavioral economics, Experimental economics