The Organization of Supplier Networks: Effects of Delegation and Intermediation

In a one‐principal two‐agent model with adverse selection and collusion among agents, we show that delegating to one agent the right to subcontract with the other agent always earns lower profit for the principal compared with centralized contracting. Delegation to an intermediary is also not in the principal's interest if the agents supply substitutes. It can be beneficial if the agents produce complements and the intermediary is well informed.     

Competition for a Majority

We define the class of two‐player zero‐sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For such games, we establish sufficient conditions for existence of a value of the game, maximin and minimax strategies for the players, and a Nash equilibrium. If all discontinuities favor one player, then a value exists and that player has a maximin strategy. A property called payoff approachability implies existence of an equilibrium, and that the resulting value is invariant: games with the same payoffs at points of continuity have the same value and ɛ‐equilibria. For voting games in which two candidates propose policies and a candidate wins election if a weighted majority of voters prefer his proposed policy, we provide tie‐breaking rules and assumptions about voters' preferences sufficient to imply payoff approachability. These assumptions are satisfied by generic preferences if the dimension of the space of policies exceeds the number of voters; or with no dimensional restriction, if the electorate is sufficiently large. Each Colonel Blotto game is a special case in which each candidate allocates a resource among several constituencies and a candidate gets votes from those allocated more than his opponent offers; in this case, for simple‐majority rule we prove existence of an equilibrium with zero probability of ties.     

Do Markets Favor Agents able to Make Accurate Predictions?

Blume and Easley (1992) show that if agents' have the same savings rule, those who maximize the expected logarithm of next period's outcomes will eventually hold all wealth (i.e. are ‘most prosperous’). However, if no agent adopts this rule then the most prosperous are not necessarily those who make the most accurate predictions. Thus, agents who make inaccurate predictions need not be driven out of the market. In this paper, it is shown that, among agents who have the same intertemporal discount factor (and who choose savings endogenously), the most prosperous are those who make accurate predictions. Hence, convergence to rational expectations obtains because agents who make inaccurate predictions are driven out of the market.     

Reverse Auctions with Multiple Reinforcement Learning Agents*

Reverse auctions in business‐to‐business (B2B) exchanges provide numerous benefits to participants. Arguably the most notable benefit is that of lowered prices driven by increased competition in such auctions. The competition between sellers in reverse auctions has been analyzed using a game‐theoretic framework and equilibria have been established for several scenarios. One finding of note is that, in a setting in which sellers can meet total demand with the highest‐bidding seller being able to sell only a fraction of the total capacity, the sellers resort to a mixed‐strategy equilibrium. Although price randomization in industrial bidding is an accepted norm, one might argue that in reality managers do not utilize advanced game theory calculations in placing bids. More likely, managers adopt simple learning strategies. In this situation, it remains an open question as to whether the bid prices converge to the theoretical equilibrium over time. To address this question, we model reverse‐auction bidding behavior by artificial agents as both two‐player and n‐player games in a simulation environment. The agents begin the game with a minimal understanding of the environment but over time analyze wins and losses for use in determining future bids. To test for convergence, the agents explore the price space and exploit prices where profits are higher, given varying cost and capacity scenarios. In the two‐player case, the agents do indeed converge toward the theoretical equilibrium. The n‐player case provides results that reinforce our understanding of the theoretical equilibria. These results are promising enough to further consider the use of artificial learning mechanisms in reverse auctions and other electronic market transactions, especially as more sophisticated mechanisms are developed to tackle real‐life complexities. We also develop the analytical results when one agent does not behave strategically while the other agent does and show that our simulations for this environment also result in convergence toward the theoretical equilibrium. Because the nature of the best response in the new setting is very different (pure strategy as opposed to mixed), it indicates the robustness of the devised algorithm. The use of artificial agents can also overcome the limitations in rationality demonstrated by human managers. The results thus have interesting implications for designing artificial agents in automating bid responses for large numbers of bids where human intervention might not always be possible.     

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.     

Push and Pull Contracts in a Local Supply Chain with an Outside Market*

Wholesale price contracts are widely studied in a single supplier‐single retailer supply chain, but without considering an outside market where the supplier may sell if he gets a high enough price and the retailer may buy if the price is low enough. We fill this gap in the literature by studying push and pull contracts in a local supplier–retailer supply chain with the presence of an outside market. Taking the local supplier's maximum production capacity and the outside market barriers into account, we identify the Pareto set of the push and/or pull contracts and draw managerial implications. The main results include the following. First, the most inefficient point of the pull Pareto set cannot always be removed by considering both the push and pull contracts. Second, the supplier's production capacity plays a significant role in the presence of an outside market; it affects the supplier's negotiating power with the retailer and the coordination of the supply chain can be accomplished only with a large enough capacity. Third, the import and export barriers influence the supply chain significantly: (i) an export barrier in the local market and the supplier's production capacity influence the supplier's export strategy; (ii) a low import (resp., export) barrier in the local market can improve the local supply chain's efficiency by use of a push (resp., pull) contract; and (iii) a high import (resp., export) barrier in the local market encourages the supplier (resp., retailer) to bear more inventory risk.     

Strategy-proof and Symmetric Social Choice Functions for Public Good Economies

We study economies with one private good and one pure public good, and consider the following axioms of social choice functions. Strategy-proofness says that no agent can benefit by misrepresenting his preferences, regardless of whether the other agents misrepresent or not, and whatever his preferences are. Symmetry says that if two agents have the same preference, they must be treated equally. Anonymity says that when the preferences of two agents are switched, their consumption bundles are also switched. Individual rationality says that a social choice function never assigns an allocation which makes some agent worse off than he would be by consuming no public good and paying nothing. In Theorem 1, we characterize the class of strategy-proof, budget-balancing, and symmetric social choice functions, assuming convexity of the cost function of the public good. In Theorem 2, we characterize the class of strategy-proof, budget-balancing, and anonymous social choice functions. In Theorem 3, we characterize the class of strategy-proof, budget-balancing, symmetric, and individually rational social choice functions.     

Market Good Flexibility in Capacity Auctions

We consider the allocation of limited production capacity among several competing agents through auctions. Our focus is on the contribution of flexibility in market good design to effective capacity allocation. The application studied is a capacity allocation problem involving several agents, each with a job, and a facility owner. Each agent generates revenue by purchasing capacity and scheduling its job at the facility. Ascending auctions with various market good designs are compared. We introduce a new market good that provides greater flexibility than those previously considered in the literature. We allow ask prices to depend both on agents’ utility functions and on the number of bids at the previous round of the auction, in order to model and resolve resource conflicts. We develop both optimal and heuristic solution procedures for the winner determination problem. Our computational study shows that flexibility in market good design typically increases system value within auctions. A further increase is achieved if each agent is allowed to bid for multiple market goods at each round. On average, the multiple flexible market goods auction provides over 95% of the system value found by centralized planning.     

Competitive Division of a Mixed Manna

A mixed manna contains goods (that everyone likes) and bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homogeneous of degree 1 and concave (and monotone), the competitive division maximizes the Nash product of utilities (Gale–Eisenberg): hence it is welfarist (determined by the set of feasible utility profiles), unique, continuous, and easy to compute. We show that the competitive division of a mixed manna is still welfarist. If the zero utility profile is Pareto dominated, the competitive profile is strictly positive and still uniquely maximizes the product of utilities. If the zero profile is unfeasible (for instance, if all items are bads), the competitive profiles are strictly negative and are the critical points of the product of disutilities on the efficiency frontier. The latter allows for multiple competitive utility profiles, from which no single‐valued selection can be continuous or resource monotonic. Thus the implementation of competitive fairness under linear preferences in interactive platforms like SPLIDDIT will be more difficult when the manna contains bads that overwhelm the goods.     

Designing Multi‐Attribute Procurement Mechanisms for Assortment Planning

This research investigates how to design procurement mechanisms for assortment planning. We consider that a retailer buys directly from a manufacturer who possesses private information about the per‐unit variable cost and per‐variety setup cost. We first develop a screening model to assist the retailer in integrating assortment planning into supply chain contracting processes when only one manufacturer is available. We demonstrate that the screening mechanism is optimal among all feasible procurement strategies. When there are multiple competing manufacturers, we propose a supply contract auctioning mechanism and evaluate its performance. In this mechanism, the retailer announces a contract menu and the manufacturer that bids the highest upfront fee paid to the retailer wins the auction. The winner then chooses and executes a contract from the contract menu. We show that when the retailer uses the optimal screening contract menu as the object of the auction, it achieves the optimal procurement outcome if the screening contract menu does not pay rent to any manufacturer type. This finding sheds light on the connection between screening and auction mechanisms when there exists multi‐dimensional private information.     

Monotonicity and Implementability

Consider an environment with a finite number of alternatives, and agents with private values and quasilinear utility functions. A domain of valuation functions for an agent is a monotonicity domain if every finite‐valued monotone randomized allocation rule defined on it is implementable in dominant strategies. We fully characterize the set of all monotonicity domains.     

Information and Efficiency in Tender Offers

We analyze tender offers where privately informed shareholders are uncertain about the raider's ability to improve firm value. The raider suffers a “lemons problem” in that, for any price offered, only shareholders who are relatively pessimistic about the value of the firm tender their shares. Consequently, the raider finds it too costly to induce shareholders to tender when their information is positive. In the limit as the number of shareholders gets arbitrarily large, when private benefits are relatively low, the tender offer is unsuccessful if the takeover has the potential to create value. The takeover market is therefore inefficient. In contrast, when private benefits of control are high, the tender offer allocates the firm to any value‐increasing raider, but may also allow inefficient takeovers to occur. Unlike the case where all information is symmetric, shareholders cannot always extract the entire surplus from the acquisition.     

Stochastic Choice and Consideration Sets

We model a boundedly rational agent who suffers from limited attention. The agent considers each feasible alternative with a given (unobservable) probability, the attention parameter, and then chooses the alternative that maximizes a preference relation within the set of considered alternatives. We show that this random choice rule is the only one for which the impact of removing an alternative on the choice probability of any other alternative is asymmetric and menu independent. Both the preference relation and the attention parameters are identified uniquely by stochastic choice data.     

Power Structure and Profitability in Assembly Supply Chains

This paper studies the impact of supply chain power structure on firms' profitability in an assembly system with one assembler and two suppliers. Two power regimes are investigated—in a Single Power Regime, a more powerful firm acts as the Stackelberg leader to decide the wholesale price but not the quantity whereas in a Dual Power Regime, both the price and quantity decisions are granted to the more powerful firm. Tallying the power positions of the three firms, for each power regime we study three power structures and investigate the system's as well as the firms' preference of power. We find that when the assembler is the most powerful firm among the three, the system‐wide profit is the highest and so is the assembler's profit. The more interesting finding is that, if the assembler is not the most powerful player in the system, more power does not necessarily guarantee her a higher profit. Similarly, a supplier's profit can also decrease with the power he has. These results contrast with the conclusion for serial systems, where a firm always prefers more power. We also find that when both suppliers are more (less) powerful than the assembler, it can be beneficial (indifferent) for everyone if the two suppliers merge into a mega supplier to make decisions jointly. When the assembler is more powerful than one supplier and less so than the other, it is always better for the system to have the two suppliers merge, and for each individual firm, merging is preferred if the firm becomes the more powerful party after merging.     

Against the De Minimis Principle

According to the class of de minimis decision principles, risks can be ignored (or at least treated very differently from other risks) if the risk is sufficiently small. In this article, we argue that a de minimis threshold has no place in a normative theory of decision making, because the application of the principle will either recommend ignoring risks that should not be ignored (e.g., the sure death of a person) or it cannot be used by ordinary bounded and information-constrained agents.     

Axioms for Deferred Acceptance

The deferred acceptance algorithm is often used to allocate indivisible objects when monetary transfers are not allowed. We provide two characterizations of agent‐proposing deferred acceptance allocation rules. Two new axioms—individually rational monotonicity and weak Maskin monotonicity—are essential to our analysis. An allocation rule is the agent‐proposing deferred acceptance rule for some acceptant substitutable priority if and only if it satisfies non‐wastefulness and individually rational monotonicity. An alternative characterization is in terms of non‐wastefulness, population monotonicity, and weak Maskin monotonicity. We also offer an axiomatization of the deferred acceptance rule generated by an exogenously specified priority structure. We apply our results to characterize efficient deferred acceptance rules.     

On the Effects of Capacity Agent on Market Equilibrium

We consider a setting of two firms and one capacity agent. Each firm serves a primary market, and the capacity agent sustains a common market to draw demand for capacity from the external firms. The firms can partner with the capacity agent under her contract to serve the common market. When they use the common market mainly as an outlet for their unused capacities, the capacity agent will only specify a variable fee for each capacity unit deployed through her, and prefer to partner with one firm in most circumstances. When the firms adjust capacities to accommodate the businesses created by serving the common market, the capacity agent will specify a lump‐sum payment and a variable fee, and will be more likely to incentivize only one firm to partner with her, when the common market is sufficiently large or the demands in the common and primary markets are strongly correlated. She will always use a fixed fee to extract, while not necessarily all, the profit gains to the firms serving the common market, but will use a variable fee only when partnering with both firms. The key results are robust with respect to market configuration and contract type.     

Peer Pressure

We present a model where agents care about their neighbors' actions and can pressure them to take certain actions. Exerting pressure is costly for the exerting agent and it can impact the pressured agents by either lowering the cost of taking the action (which we call “positive pressure”) or else by raising the cost of not taking the action (which we call “negative pressure”). We show that when actions are strategic complements, agents with lower costs for taking an action pressure agents with higher costs, and that positive pressure can improve societal welfare. More generally, we detail who gains and who loses from peer pressure, and identify some circumstances under which pressure results in fully (Pareto) optimal outcomes as well as circumstances where it does not. We also point out differences between positive and negative pressure. (JEL: Z13, D62, C72, D85)     

Scheduling two job families on a single machine with two competitive agents

We consider the scheduling problems arising when two agents, each with a family of jobs, compete to perform their respective jobs on a single machine. A setup time is needed for a job if it is the first job to be processed on the machine or its processing on the machine follows a job that belongs to another family. Each agent wants to minimize a certain cost function, which depends on the completion times of its jobs only. The aim is to find a schedule for all the jobs of the two agents that minimizes the objective of one agent while keeping the objective of the other agent being bounded by a fixed value \(Q\). Polynomial-time and pseudo-polynomial-time algorithms are designed to solve the problem involving various combinations of regular scheduling objective functions.     

复杂不确定环境下考虑代理人通过努力减少项目持续期限的最优代理合同

本文着重研究复杂不确定环境下如何设计最优合同,以激励代理人减少项目持续期限。在代理问题中,以往的数量研究大多使用随机变量刻画项目参数和代理人的努力程度。但是,在某些情况下,项目参数和代理人的努力程度不能被历史数据获得,而必须由专家进行估计。运用不确定变量刻画专家对这些参数的估计,并且证明这样做是合理的。通过应用不确定理论,提出复杂不确定环境下考虑代理人通过努力减少项目持续期限的最优代理合同模型。之后,为了解决这个问题,给出了该模型的确定性形式。此外,对是否考虑代理人不确定努力的最优合同进行了比较。结果显示,当其他条件相同时,委托人在考虑代理人不确定努力程度的合同中得到的期望收益不低于在没有考虑代理人不确定努力程度的合同中到的期望收益。最后,为了更好地展示模型的应用,给出了一个数值例子并进行了相关讨论。