Decisions of persons, the pharmaceutical industry, and donors in disease contraction and recovery assuming virus mutation

Background The article develops an eight-period game between N persons and a pharmaceutical company. The choices of a donor and Nature are parametric. Methods Persons choose between safe and risky behavior, and whether or not to buy drugs. The pharmaceutical company chooses whether or not to develop drugs. The donor chooses parametrically whether to subsidize drug purchases and drug developments. Nature chooses disease contraction, recovery, death, and virus mutation. The game is solved with backward induction. Results The conditions are specified for each of seven outcomes ranging from safe behavior to risky behavior and buying no or one or both drugs. The seven outcomes distribute themselves across three outcomes for the pharmaceutical company, which are to develop no drugs, develop one drug, and develop two drugs if the virus mutates. For these three outcomes the donor’s expected utility is specified. Conclusion HIV/AIDS data is used to present a procedure for parameter estimation. The players’ strategic choices are exemplified. The article shows how strategic interaction between persons and a pharmaceutical company, with parametric choices of a donor and Nature, impact whether persons choose risky or safe behavior, whether a pharmaceutical company develops no drugs or one drug, or two drugs if a virus mutates, and the impact of subsidies by a donor.

Water Scarcity and Conflict Between Upstream and Downstream Riparian Countries

More than one-quarter of the world’s population lives in water-scarce areas, while most countries share at least one transboundary river. If water scarcity is this prevalent, should we expect riparian countries to fight over the water allocation of shared rivers? To answer this question, I develop a modified one-shot three-stage river-sharing game where countries can resort to force to solve their water allocation problem. Using backward induction, I solve for the probability of the downstream country initiating conflict against the upstream country and the likelihood of the latter responding with force to the former’s hostile actions. I test the model empirically using a set of all upstream–downstream riparian dyads with available data from AQUASTAT and the Correlates of War Project for the years 1960–2010. The main contribution of this paper is that it demonstrates how upstream and downstream riparian countries differ in their decision to use force against the other country when experiencing water scarcity. I find that water scarcity increases the likelihood of the downstream country initiating the conflict, but it has no effect on the upstream country’s likelihood of responding with force. If history is a predictor of the future, then the results imply that as more riparian countries become water-scarce, militarized conflicts between upstream and downstream countries are likely to increase, especially if there is heterogeneity in water availability between the riparian dyad.

Analysis of Asymmetric Quantity Commitment in Decentralized Supply Chains

Quantity commitment chosen by firms in competition has been demonstrated by previous studies to mitigate price competition. This study demonstrates that asymmetric quantity commitment can always arise when one firm (e-tailer) shortens lead times or adopts just-in-time systems to circumvent quantity commitment while another firm (retailer) does not. To study the asymmetric quantity commitment in decentralization, a multi-stage game is analyzed, and backward induction is adopted. The authors find that the retailer always adopts the quantity commitment in the decentralization to achieve a higher profit.

Dynamic consistency, valuable information and subjective beliefs

Ambiguity sensitive preferences must fail either Consequentialism or Dynamic Consistency (DC), two properties that are compatible with subjective expected utility and Bayesian updating, while forming the basis of backward induction and dynamic programming. We examine the connection between these properties in a general environment of convex preferences over monetary acts and find that, far from being incompatible, they are connected in an economically meaningful way. In single-agent decision problems, positive value of information characterises one direction of DC. We propose a weakening of DC and show that one direction is equivalent to weakly valuable information, whereas the other characterises the Bayesian updating of the subjective beliefs which are revealed by trading behavior.

The Implication of Channel Discrepancy in a Dual-Channel Supply Chain

This paper studies the implication of channel discrepancy between the retail and direct channels in a dual-channel supply chain consisting of one common retailer and two manufacturers in which the manufacturers may have different market powers. Each manufacturer provides a substitutable product and opens an online channel to customers directly. We develop an analytical model to derive the optimal pricing strategies by using game theory and the backward induction method, and we examine related properties under three market power structures while considering channel discrepancy, including the Nash equilibrium, the Manufacturers leader Stackelberg, and the M1 leader Stackelberg models (denoted as the N, MS, and M1S models, respectively). Numerical simulations are examined to reveal and verify the effect of channel discrepancy on optimal prices, demands, and profits. We find that a higher level of channel discrepancy induces higher prices, demands, and profits for each member in both channels, while this kind of stimulating impact for the leader manufacturer who obtains a higher level of channel discrepancy will be more significant than it is for the other members in the three models. In addition, the profit of the supply chain in the N model is always higher than it is in the MS model, while it may be higher or lower than it is in the M1S model depending on the level of channel discrepancy.

On the correctness of monadic backward induction

In control theory, to solve a finite-horizon sequential decision problem (SDP) commonly means to find a list of decision rules that result in an optimal expected total reward (or cost) when taking a given number of decision steps. SDPs are routinely solved using Bellman’s backward induction. Textbook authors (e.g. Bertsekas or Puterman) typically give more or less formal proofs to show that the backward induction algorithm is correct as solution method for deterministic and stochastic SDPs. Botta, Jansson and Ionescu propose a generic framework for finite horizon, monadic SDPs together with a monadic version of backward induction for solving such SDPs. In monadic SDPs, the monad captures a generic notion of uncertainty, while a generic measure function aggregates rewards. In the present paper, we define a notion of correctness for monadic SDPs and identify three conditions that allow us to prove a correctness result for monadic backward induction that is comparable to textbook correctness proofs for ordinary backward induction. The conditions that we impose are fairly general and can be cast in category-theoretical terms using the notion of Eilenberg–Moore algebra. They hold in familiar settings like those of deterministic or stochastic SDPs, but we also give examples in which they fail. Our results show that backward induction can safely be employed for a broader class of SDPs than usually treated in textbooks. However, they also rule out certain instances that were considered admissible in the context of Botta et al. ’s generic framework. Our development is formalised in Idris as an extension of the Botta et al. framework and the sources are available as supplementary material.

Dynamic channel decision-making of fresh agricultural product companies considering consumer convenience preferences

This paper studies the strategic channel decision-making of fresh agricultural product enterprises from the perspective of consumer convenience perferences. This research is carried out under the background of the upgrading of domestic consumption and explosion of stay-at-home economy in china in recent yeas. In this paper,consumers are segmented firstly according to their different preference for consumption time,namely,convenience preference. Then, a channel decision model which consiers the convenience sensitivity of consumers and the inconvenience cost is proposed. Finally, the optimal wholersale price and delivery lead time of the supplier and the service level decision of the retailer are obtained by using backward induction method. The results show that under different market conditions, the supplier can adopt three equilibrium strategies:NR(No Retailer),CP(Capture Profit) and SP(Share Profit). With the change of inconvenience cost, the equilibrium state of supply chain will also change. Fresh agricultural product companies can choose different strategies to maximize their revenue according to different markets.

Two-Player Location Game in a Closed-Loop Market with Quantity Competition

This paper considers the two-player location game in a closed-loop market with quantity competition. Based on the Cournot and Hotelling models, a circle model is established for a closed-loop market in which two players (firms) play a location game under quantity competition. Using a two-stage (location-then-quantity) pattern and backward induction method, the existence of subgame-perfect Nash equilibria is proved for the location game in the circle model with a minimum distance transportation cost function. In addition, sales strategies are proposed for the two players for every local market on the circle when the players are in the equilibrium positions. Finally, an algorithm for simulating the competitive dynamics of the closed-loop market is designed, and two numerical simulations are provided to substantiate the effectiveness of the obtained results.