2 The Institutional View on Markets
2.1 Microeconomic System Framework
2.1.6 System Performance
Institutions are introduced to attain a desired set of objectives. The objectives pertain to the outcome that results from agent interaction along the message exchange process. Clearly, the institutions are not intended to attain these goals at random but rather frequently. In other words, the institution must set the right incentives such that agents behave in a certain way, that the (game-theoretic) equilibrium corresponds with an outcome, i.e. allocation and prices that satisfy the desired set of goals. Setting the right incentives is not easy as they are depend-ent on the economic environmdepend-ent.
In this context the notion of the term mechanism can be introduced that combines the institu-tion and the economic environment. Broadly speaking, a mechanism describes the procedure by which the agents can realize an allocation. In game-theoretic terms the mechanism deter-mines the rules of a game. Once this mechanism is set up, the agents submit their correspond-ing (equilibrium) messages (i.e. strategies) and receive their allocation share. Apparently, mechanisms are mappings from preferences, and each agent’s information or beliefs about other agents, into allocations (Smith 2003b). Mechanisms create thus the connection between
the economic environment via the messages (agent behavior) and the outcome dependent on the institutions.47
A mechanism M specifies the available messages and the rules how to resolve it via choice and transfer rules: For any message profile m =(m1, m2, …,mn) the mechanism M computes the resulting allocation and transfers as an equilibrium solution.
Definition 8: Mechanism
A mechanism M is a pair (M, yM) where M is the message space (language) and yM the re-sulting choices and transfers.
Mechanisms thus create the relationship between the institution and the economic environ-ment on the one hand and the outcome on the other hand. The system performance now meas-ures the outcomes with respect to the economic environment. The outcome refers to the dis-tribution of resources and the corresponding transfers, which is determined by
(
h ( ),h ( ),...,h ( ),...,t ( ),t ( ),...,t ( ))
) (
ySCF θ = 1 θ 2 θ n θ 1 θ 2 θ n θ . This function ySCF(θ) is in litera-ture termed social choice function. Note that the social choice function calculates the outcome as a function of the preferences and not as a function of the messages. As Figure 2 proposes, comparing the actual outcome with the social choice function yields the assessment of the goodness of the applied mechanism. In other words, there is generally an evaluation function,
) , X (
U θ , which “tells the designer how to value particular outcomes” (Ledyard 1993, 127) with respect to the environment. Purely allocation-oriented measures may, however, ignore that mechanism itself can create frictions or so-called transaction costs are defined as the costs of running an microeconomic system (Arrow 1969). Transaction costs occur on a transaction, i.e. on the exchange of resources; as such they diminish the benefits from trade. A reduction of those frictional costs would consequently increases the individual gains drawn from trade and thus social welfare (Coase 1937). A performance measure should ideally not only take allocations but also the mechanisms into consideration. Apparently, transaction costs are such a comprehensive performance measure. To make transaction costs more manageable, they are split into coordination and motivation costs (Milgrom and Roberts 1992).48:
• Coordination costs arise from the need to determine the allocation and transfer payments and other details of the transaction, such as bringing buyers and sellers together. This means coordination costs comprise both allocation as well as mechanism-oriented aspects.
For example, the transaction costs for a buyer are the price he has to pay for a good and the time he spent searching for a corresponding partner.
• Motivation costs are associated with informational incompleteness and asymmetries and imperfect commitment. Informational incompleteness and asymmetries refer to situations where the participating agents do not have all relevant information. Due to the lack of this relevant information they cannot determine whether the terms of the agreement are mutu-ally acceptable. The agreement can – although beneficial for all participating agents – fail, as the agents may fear to be shortchanged. Alternatively, the agents can make costly pro-tections against shortchanging, which basically are transaction costs. Imperfect
47 The way a resource allocation mechanism works is not independent of the domain, which is represented by the economic environment. A resource allocation mechanism yields different outcomes when applied on a different class of environments. As such, the study of mechanisms “must be made with reference to the class of environments to be covered” (Hurwicz 1959) and in the light of some performance charac-teristics.
48 Dahlman summarized transaction costs as search and information costs, bargaining and decision costs, policing and enforcement costs (Dahlman 1979).
ment refers to the inability of the participating agents of binding themselves to their an-nouncements. This inability stems from the fact that the agents once they announced ei-ther a threat or a promise, would like to renounce. For example, a supplier make a large investment in order to accommodate the specific wishes of a manufacturer. The contract between the supplier and manufacturer defines the prices the manufacturer has to pay. Af-ter the supplier has made his investment, the manufacturer may want to renegotiate the contract. As the investments are basically sunk costs, the manufacturer can force lower prices and other concessions. Prior protection against opportunistic behavior is costly, constituting also transaction costs.
As Milgrom and Roberts note is the transaction cost approach appealing, but not applicable to all problems of economic institutions (Milgrom and Roberts 1992). The primary criticism here is not associated with the concept of transaction costs, but with the desiderata that institu-tions should be designed such that those transaction costs are minimized.49 For example, why should a seller design an institution that minimizes the transaction costs of the system, con-sisting of the seller and buyers? Instead the seller presumably cares for only those costs he personally has to bear.
Group Criterion pertains to
Efficiency Allocative efficiency Informational efficiency
Allocation Mechanism
Optimality Revenue maximization Allocation
Solution Equilibrium and convergence Number of iterations
Stability
Mechanism Mechanism Allocation
Feasibility Allocative feasibility
Budget balance Informational feasibility Incentive feasibility
Allocation Allocation Mechanism Mechanism Fairness Pareto-satisfactoriness
Institutional fairness
Allocation Mechanism Tractability Simplicity
Computational tractability
Mechanism Mechanism Table 1: Objective Categories
The transaction costs approach cannot constitute the overall goal. Instead the general evalua-tion funcevalua-tion U(X,θ ) can comprise various objectives or desiderata. The following discuss-ing attempts to describe the most commonly desiderata for the evaluation function used in literature. The goals are classified into six groups according to their scope as Table 1 illus-trates.
The first column describes the general category of goals; its sub-goals are further shown in the second column. The last column exhibits whether the goal pertains to the mechanism or to the resulting allocation.
2.1.6.1 Efficiency
In general efficiency denotes the capacity to produce desired results with a minimum expendi-ture of energy, time, or resources (Merriam-Webster 2002).
49 In fact, there are more limitations of the transaction cost approach (see for example Milgrom and Roberts 1992).
Principally, the following two criteria can be defined:
• Allocative Efficiency
• Informational efficiency
Allocative efficiency is a very old and well-defined concept in Economics. Traditional welfare theory provides measures and criteria to evaluate and compare different allocations in micro-economic systems. There are several efficiency criteria, but most of those are fairly restrictive and bear some problems in their general applicability. The most common efficiency criterion is that of Pareto-efficiency. Pareto efficient resource allocation denotes an allocation, for which no other allocation exists, that makes at least one agent better off without making at least one agent worse off.
efficiency is often mistakenly listed as a mechanism property. However, Pareto-efficiency refers to the imputed allocation and not to the mechanism. Pareto Pareto-efficiency can be defined in an ex-post and ex-ante sense. Ex-ante efficiency takes preferences over expected allocations in consideration, whilst ex-post analyzes preferences over realized allocations.
A mechanism that maximizes the sum of individual utilities (i.e. the sum of surpluses condi-tional on the given information set) is called efficient. This efficiency concept commonly used in mechanism and auction theory corresponds with Pareto-efficiency only when utility is transferable among the agents.
Remark 2.1-4: Efficiency and Common Values
In the case of the pure common value model (see Example 2.1-3) the issue of efficiency becomes trivial, as any outcome that assigns the resources with the probability 1 to an agent is efficient. This is intuitive since all agents have the same (common) valuation (McLean and Postlewaite 2003).
Informational efficiency pertains to the issue of decentralization of information and to the lim-ited information processing capacity of the agents (Hurwicz 1972; Hurwicz 1973). In order to explain the notion of informational efficiency, it is convenient to discuss the effect of different environments on the informational efficiency if the same mechanism is applied. Subsequently, the concept can be used to compare different mechanisms:
The informational burden a mechanism creates is dependent on the underlying environment:
If information is fully decentralized, as it is the case in an informationally decentralized envi-ronment, a mechanism causes a higher informational burden as if information would be fully centralized. The intuition for this lower burden of a fully centralized environment is straight-forward: The informational burden is lessened, since no information must be transmitted tothe mechanism. Furthermore, the agent decision problem50 is per definition resolved at no costs.
As the mechanism knows all local environments, the valuation problem, i.e. the computation of the preferences and the bidding problem, i.e. the computation of the best strategy depend-ent on the preferences, vanish. In decdepend-entralized environmdepend-ents this agdepend-ent decision problem and the corresponding deliberation costs naturally become more severe as the information proc-essing capacity of the agents is limited.
This instructive example shows that the informational burden can be defined on the basis of communication and deliberation costs. Those costs are here used as a broad concept and refer to all tasks connected with communication and information processing. That means they comprise all costs that are related with tasks such as “communicating”, “observing”, and
“computing” to name a few.
50 Generally the agent decision problem is separable into a valuation and a bidding problem (Parkes 2001).
Apparently, not only the underlying environment but also the applied mechanism determines the amount of informational efficiency. Given the same environment, there exist a variety of mechanisms that achieve the same outcome (i.e. Pareto efficient allocation). However, those mechanisms can be ordered based on their informational efficiency. The objective of a mechanism designer should be “design a mechanism that (1) attains a desired allocation, and, (2) is informationally efficient”.
Searching for a mechanism that is efficient with respect to all components of communication and deliberation costs appears to be extremely difficult. In literature those costs are frequently measured in terms of the size of the message space M.51 Recall that the message space or lan-guage denotes the messages available to the agents. A larger message size52 therefore implies higher communication and deliberation costs: It is harder for the agent to conceive the mean-ing of the message and also to identify what action to be taken as a reaction of the message.
Now, the objective of the mechanism designer can be refined to “design a mechanism that attains a desired allocation with a minimal message space size”.
However, since long messages can be expressed by a sequence of small messages from small message spaces, this measure appears to be meaningless if no further restrictions are intro-duced.53 The restrictions may basically pertain to the adjustment process rules or choice rules.
For example, one restriction could require that only the last message sent by each agent are taken into consideration (Mount and Reiter 1974; Van Zandt 1999; Hurwicz and Marschak 2001).
Recently, the newly developing scientific branch of computational mechanism design renews the idea of informational efficiency. The underlying assumption is that the communication requirements may themselves constitute a ‘bottleneck’ that prevents efficiency (Gomber, Schmidt et al. 2000; Nisan and Segal 2003).
2.1.6.2 Optimality
The objective of optimality commonly refers to the maximization of the revenues a selling agent can earn in a mechanism. An optimal mechanism is the one, which maximizes the total revenue. In the single unit case under the assumptions of the IPV, efficiency corresponds with optimal auctions (Milgrom 1989). However, in more complex environments (e.g. multi unit cases) this does not necessarily hold. When resources are complementarities, that is the valua-tion for resource a and b together in a bundle exceeds the valuavalua-tions of its parts va + vb < va+b
(i.e. informational externalities) it is possible that there is a trade-off between efficiency and optimality.
Example 2.1-23: Trade-Off between optimality and efficiency
Assume there are two resources a and b and two buying agents competing against each other. Agent I values resource a 10 € and b 7 €, whereas agent II values a 8 € and b 12 €.
An efficient mechanism awards a to I and b to II, as this combination maximizes the sum of valuations. The corresponding revenue the seller can get is 15 € which is the sum of the rejected bids. The seller could raise his revenue by selling both resources as a package to agent II. The revenue would amount to 17 € being the highest rejected bid. Apparently, there is a trade-off between efficiency and optimality (Jehiel and Moldovanu 2003).
51 See for example Mount and Reiter (Mount and Reiter 1974).
52 Hurwicz proposes the dimension of Euclidian spaces as a measure of size (Hurwicz 1959). For an exten-sion to topological spaces see (Mount and Reiter 1974).
53 Mount and Reiter note in their footnote that “certain additional restrictions are need to avoid anomalies arising from the fact that arbitrary amounts of information can be encoded in a single real number”
(Mount and Reiter 1974, 165).
2.1.6.3 Solution
The solution criteria investigate the properties of the allocation such as occurrence likelihood or stability. The criteria comprise the following:
• Equilibrium and Convergence
• Number of iterations
• Stability and the “core”
In equilibrium no agent would find it in his interest to unilaterally change his behavior. In other words, equilibrium denotes a state where no agent wishes to depart from. For example, if the mechanism proposes an allocation based on the received offers, the agents may have the chance to adjust their offers to the new information.54 If the mechanism proposes an allocation such that each agent would agree to choose its part, the mechanism attained equilibrium (Varian 1992; Wellman and Wurman 1998). Such a situation is highly desirable if the alloca-tion itself meets certain criteria such as allocative efficiency. There are many (game-theoretic) equilibrium concepts discussed in literature.55 Standard equilibrium concepts that play a role in this book are the following three:
• Nash Equilibrium
As in the above description, a Nash equilibrium is characterized by the fact that all agents cannot increase their utility by unilaterally changing their behavior.
• Bayesian-Nash Equilibrium
A strategy profile m is in Bayesian-Nash equilibrium if for all agents the expected utility over all types derived from the chosen strategy is greater than those derived from any other strategy.
• Dominant Strategy Equilibrium
A dominant strategy m* maximizes the utility of agent regardless what strategies the other agents play. Hence, a dominant strategy equilibrium is an equilibrium in which all agents play their dominant strategy.
The existence of an equilibrium given a certain mechanism is applied in a specified economic environment is necessary but not sufficient that this equilibrium state is really achieved. The requirement of convergence simply states that the mechanism approaches an equilibrium allo-cation over time.
Mechanisms are often iterative. That means they accept messages on each round and an-nounces a provisional winning allocation. The mechanism stops when equilibrium is reached.
The number of iterations confines the rounds necessary to approach equilibrium. Malinvaud formulated a desideratum that the mechanism yields a feasible solution within a finite number of iterations (Hurwicz 1973). Accordingly, the mechanism should not only converge to an existing equilibrium but also in an acceptable amount of time. Malinvaud, for example, shows that some adjustment processes fail to attain a feasible allocation if the process is interrupted after a finite number of iterations. In this tradition the number of iterations are sometimes termed Malinvaud’s criteria (Hurwicz 1969).
54 Using game-theoretic reasoning, the mechanism must not take place in iterations. The process can also occur as calculations in the head of the agents. An agent can predict the equilibrium, and also that the opponents predict it, and so on. If all agents predict it right that particular (Nash) equilibrium will occur (Fudenberg and Tirole 2000).
55 For a comprehensive overview see Fudenberg and Tirole (Fudenberg and Tirole 1983).
Stability or being in the core requires that all agents cannot increase their individual utility by not participating. If the resulting allocation is unacceptable to some group (coalition) of agents since they can increase the utility for the members of this group, it is unstable. Such instable allocations are dominated. The set of all undominated allocations originates the core.
If a solution is in the core it is automatically Pareto-efficient; though the converse is not true.
The concept of the core comes from coalitional game theory and provides a useful tool for mechanism design, as it demonstrates whether a mechanism evolves: If the economic envi-ronment has an empty core, no such mechanism would emerge (Telser 1994; Nyshadham and Raghavan 2001; Roth 2002).
Remark 2.1-5: Individual Rationality and Stability
The constraint that the mechanism is individual rational requires the solution to be stable for the coalition size of 1. This implies that the agent is not worse off than initially. The utility after participating in the mechanism must be higher than before. Otherwise the agent would decide not to take part in the mechanism. This individual rationality con-straint is thus sometimes termed participation concon-straint (Wurman 1999; Fudenberg and Tirole 2000).
2.1.6.4 Feasibility
Feasibility criteria deal with the question whether a mechanism or an allocation is technically implementable. An allocation is only feasible if it does not distribute more (either transfer payments or resources) than is available. Mechanism-oriented feasibility is concerned with the question whether some outcome, given by the social choice function can be implemented, with respect to information and incentives. As such, the message space and the outcome func-tion are analyzed whether they can achieve the desired outcome.
Feasibility objectives are the following:
• Allocative feasibility
• Budget balance
• Informational feasibility
• Incentival feasibility (incentive compatibility)
Before the quality of an allocation is analyzed, it is important to know whether the allocation is allocative feasible. In other words, allocative feasibility requires that the allocated resources are actually available. In exchange environments allocative feasibility is fairly easy to keep track of: The mechanism simply cannot assign more resource than the initial endowment.
However, if production is possible the interdependence between inputs and outputs can be difficult to monitor: for example, if agent i can produce X only if it gets Y and X and Y are allocated by the same mechanism (Wellman and Wurman 1998).
Furthermore, budget balance is concerned whether the mechanism requires transfer payments from outside the system. A mechanism is said to be budget balanced if the amount of transfers sum up to 0 over all agents 0
1
∑
== N
i
ti . In this case the mechanism ‘merely’ redistributes the payments among the agents. Neither funds are removed from the system nor is the system subsidized from outside. Budget balance is a nice property since the resource allocation can be performed at no costs. In case the transfers result in a surplus N t 0
1 i
i <
∑
=funds are taken
away from the system and given to some outsider. Returning the surplus to the system would exacerbate the incentival impact of the mechanism. In the case the mechanism runs a deficit
0 t
N
1 i
i >
∑
=the mechanism must be subsidized by some outside source and is thus not per-se feasible. In both cases the allocative efficiency of the resource allocation is distorted: Deficits must be financed by some sort of tax, which creates new distortions. Surpluses must be given away also leading to distortions (Parkes 2001; Jackson 2002a).
Informational feasibility imposes a lower bound on the minimal size of the message space. If the information carrying capacity represented by the message space size is insufficient, the mechanism cannot implement a specified goal. For example, if the language of a mechanism allows only for single dimensional bids, e.g. price, the communication of a production set describable by a number of real parameters is impossible. Accordingly, a mechanism, which requires production sets as inputs is not feasible (cf. chapter 2.2.1.2).
“A mechanism that is informationally feasible may be criticized on grounds of incompatibility with “natural” incentives (Hurwicz 1972, 320). Incentive feasibility or more often used in-centive compatibility refers to the validity of the messages the agents place. It is said a mecha-nism is incentive compatible if the agents report their preferences truthfully. Agents may have an incentive to untruthfully report their preferences in order to increase their individual utility.
Recall the public goods example (Example 2.1-12). If the report (message) is not only used to determine whether the project is realized but also taken as a basis for payments, the agents can increase their utility by understating their true valuation: In case the project is undertaken agent i reduces his corresponding payment by the shaded report. This misrepresentation of the agent’s valuation is individually optimal but for the society it is not since it creates an alloca-tive distortion.
Accordingly, incentive compatibility imposes an important requirement on mechanisms. The mechanism must direct the behavior of the agents to honestly reveal their preferences by set-ting adequate incentives. Designing mechanisms is thus often reduced to incentive engineer-ing.
2.1.6.5 Fairness
Fairness can refer to either the allocation or to the mechanism. Note that fairness with respect to the allocation does not demand for equal shares for all agents. It rather demands that the chances for all agents are regardless of the initial endowment equal. Fairness concerning the mechanism requires equal institutional rights. The group of fairness objectives thus compre-hends two criteria:
• Pareto satisfactoriness
• Institutional fairness
From a social welfare point of view, a Pareto-efficient allocation can be non-satisfactory. That means a very imbalanced distribution of resource is not desirable although it suffices Pareto-efficiency. In this context Hurwicz introduced the criterion of Pareto-satisfactoriness (Hurwicz 1973). Accordingly, satisfactoriness terms a mechanism that attains a efficient allocation as equilibrium. This property is called non-wasteful. Furthermore, Pareto-satisfactoriness demands that this equilibrium can be obtained by redistributions. This so-called unbiasedness requires the mechanism to equalize the chances of the agents independent of their initial endowment. Lastly, Pareto-satisfactoriness also postulates the mechanism to be