In the context of classical exchange economies, we study four ways in which agents can strategically take advantage of allocation rules by affecting who participates and on what terms (Thomson in Soc Choice Welf 42:289–311, 2014). (1) An agent transfers their endowment to someone else and withdraws. The two of them may end up controlling resources that allow them to simultaneously reach higher welfare levels than they otherwise would. (2) An agent invites someone in and let their guest use some of their (the host’s) endowment. The guest transfers back to them what they are assigned over their endowment. The host may benefit. (3) An agent withdraws with their endowment. As in (1), they and someone who stays may end up controlling resources that allow the two of them to simultaneously reach higher welfare levels than they otherwise would. (4) An agent pre-delivers to someone else the net trade that the rule would assign to that agent had the agent participated. The second agent withdraws. The first agent participates with a modified endowment. The first agent may benefit. We ask whether “the constrained priority rules”, defined by maximizing the welfare of a particular agent subject to each of the others finding their assignment at least as desirable as their endowment satisfy these various requirements. The answers are all negative. Because these types of rules are often better behaved than rules that attempt some fairness in distributing gains from trade, these results strengthen the negative conclusions reached in Thomson (2014), and they may provide the key to identifying circumstances in which rules exist that satisfy the axioms, or to proving general impossibility results.

We formulate and study the requirement on an allocation rule that no agent should be able to benefit by artificially augmenting their endowment. This can be either through simply exaggeration or through a transfer of resources from outside of the current trading partners, resources that have to be returned after the rule is applied and the agent has received their assignment. We show that the Walrasian rule is not “augmentation-proof” even on standard domains. More seriously, no efficient selection from the individual-endowments lower bounds correspondence, or from the no-envy correspondence, or from the egalitarian-equivalent correspondence is augmentation-proof. These impossibilities hold even when preferences are homothetic, and even if the agent cannot augment their endowment by more than an arbitrarily small proportion of the resources they truly own.

We consider the problem of dividing the cost of a facility when agents can be ordered in terms of the needs they have for it, and accommodating an agent with a certain need allows accommodating all agents with lower needs at no extra cost. This problem is known as the "airport problem", the facility being the runway. We review the literature devoted to its study, and formulate a number of open questions.

In the context of claims problems, we formulate an axiom of invariance of a rule with respect to its “partial implementation”: having applied the rule to a problem in its domain of definition, we imagine some claimants picking up their awards and we consider the problem of distributing what remains of the endowment among the other claimants: in this problem, the claims of the first group of claimants are set equal to zero and the endowment is adjusted down by the sum of their awards; we require of a rule that it assign to each remaining claimant the same amount as it did initially. We formulate several variants of this requirement of “partial-implementation invariance” and a “converse” of it. We investigate how the two requirements relate to known axioms and ask whether they are preserved by certain operators that have been defined on the space of rules. Our main result is a characterization in our fixed-population framework of a family of rules introduced and characterized by Young (Math Oper Res 12(3):398–414, 1987) in a variable-population framework. These rules are known under the name of “parametric rules”.

For the problem of fully allocating a social endowment of a commodity among a group of agents with single-peaked preferences, we study the consequences of manipulation for several families of rules that are not strategy-proof. Given a rule and a true preference profile, we consider the induced direct revelation game, and characterize its equilibrium allocations in terms of the profile. Our results are unequivocal: for any rule we consider, and for each true preference profile, there is a unique Nash equilibrium allocation. For the profile, it is the allocation of the uniform rule (Sprumont, 1991), the unique strategy-proof, efficient, and symmetric rule in this literature. These conclusions are drawn from two distinct sets of assumptions on the rules.

An allocation rule is “withholding-proof" if no agent ever benefits from withholding some of the resources they own, their final bundle consisting of what the rule assigns to them together with whatever they withheld. It was known that on the “classical" domain of continuous, monotone, and convex preferences, no rule is efficient and withholding-proof (Postlewaite, Rev Econ Stud 46:255–262, 1979). We show that this disappointing news persists under the simultaneous imposition of the following three restrictions: (i) the domain only consists of classical and homothetic preferences; (iii) when an agent withholds some of their endowment, they only recover a percentage of what they withhold, no matter how close to 0 that percentage is; (iii) rules are required to satisfy any of the central punctual requirements of fairness, the individual-endowments lower bounds, no-envy in trades (adapted from Tinbergen, Redelijke Inkomensverdeling, Second Edition. N.D. DeGulden Pers, Haarlem, 1953, and Foley, Yale Economic Essays 7:45–98, 1967) and egalitarian-equivalence in trades (adapted from Pazner and Schmeidler, Quart J Econ 92:671–687, 1978 and Schmeidler and Vind, Econometrica 40:637–642, 1972).

In a “queueing problem”, a group of agents are waiting for a service. Each agent incurs a cost of waiting that is proportional to the time they wait. Monetary transfers can take place. We study the subsolutions of the no-envy solution that are anonymous, consistent, conversely consistent, and continuous. We show that there are infinitely many proper consistent subsolutions from the no-envy solution and characterize a class of these solutions on the basis of basic requirements of continuity, anonymity, monotonicity with respect to the budget available, consistency, and the converse of consistency.

We consider classical problems of fair division and generalize the standard requirement on solution mappings known as “replication invariance”. Consider an economy and an allocation chosen by a solution for it. Allowing the replication parameter to vary from agent to agent, we correspondingly adjust the social endowment so that it be possible to assign to each agent and their clone(s) what the agent has been assigned at the allocation under consideration. We require that this list of assignments be chosen by the solution mapping for the resulting economy . We show various ways in which this property is related to other properties that have been discussed in the literature on economic design. We characterize the “Walrasian solution operated from equal division” on the basis of efficiency, the equal-division-lower-bound, and this property, thereby obtaining an analog of the Debreu, Scarf (Int Econ Rev 4:235–246, 1963) convergence theorem in which the no-blocking requirements that define the core are replaced by the equal-division-lower-bound. For the problem of allocating a social endowment of a single commodity among a group of agents with single-peaked preferences (Sprumont in Econometrica 59:509–519, 1991), we characterize the so-called “uniform rule” in a similar way.

At this point, it may be useful to summarize what we’ve discussed, to make a list of things to do when conducting axiomatic work in economic design.

A broad category of normative axioms are relational axioms, axioms that have to do with how solution mappings should respond to changes in the parameters of problems. They’ll be the object of our conversation today.

We study the geometry of the Pareto set in Edgeworth box economies when both agents have continuous, strictly monotonic, strictly convex, smooth, and homothetic preferences. We show that this set is either the diagonal of the box or it is a “doubly visible” curve connecting the origins of the box: imagining the curve to be opaque, an observer standing at either origin is able to see it in its entirety. We also study the case of preferences for which both goods are normal at all prices. In this case, we deduce monotonicity of the Pareto set. We also state a “converse” of each of these statements.

Research on the Southwest Asia North Africa region often focuses on turbulent upheaval and landscape change in urban areas, and less on the rural and agrarian spaces left behind. In this paper, we look at the varying trajectory of landscape change in two neighboring villages in Mount Lebanon with similar geophysical characteristics but very different ecologies and economies. We show how these paths were mediated by capital flows and the changing modes of production and livelihoods. Looking through the lens of the Agrarian Question, we argue for its continued importance in understanding rural landscapes and their place in capitalist development.

In this chapter I discuss how the axiomatic approach to economic design can be complemented with other approaches, in particular by invoking concepts and techniques of the two main branches of game theory, the cooperative branch and the non-cooperative branch. There’re several types of cooperative games, and I review the central ones. I briefly comment on the role of mathematics and on how experimental work and philosophy can help in our design endeavor. One is that it’s about conflictual situations—what we call a gameGame is a formal representation of such a situation. It’s about understanding both how people handle conflicts on their own and also about helping them come up with satisfactory resolutions of conflicts; and a central objective of economic design is to find compromises between outcomes that people value differently.

Understanding how robust a rule is to people’s attempts to affect their assignments in their own favor by being strategic instead of doing what they’re asked to do, is an important part of the research program on economic design. We can’t ignore strategic behavior. Each participant has some influence over the choices that are made by exploiting the information they hold privately concerning a variety of data about the situation and that is needed to calculate the outcomes recommended by a rule. This information certainly concerns them, primarily their preferences, but they can also exercize their influence through the resources they control. A rule should give participants the incentive to be truthful about this information and to not exercise this control. “Incentive-compatible”Incentive-compatibility is the general term that is used to designate rules that do. But there’re many ways in which someone may be strategic, and to each of them corresponds a requirement of immunity of a rule to the behavior. We’ll review them here. We’ll also propose ways of assessing the manipulability of a rule and ways of circumventing manipulation through what’s called “implementation”.

This textbook is Volume 1 of a two-volume set on the axiomatics of economic design. It introduces readers to what motivates economic design.

We consider the problem of allocating a social endowment of private goods among a group of n agents with linear preferences. We search for rules that satisfy three standard requirements. First is (Pareto-)efficiency. Second is the fairness requirement of “equal treatment of equals” (in welfare terms). Third is the incentive requirement of “strategy-proofness”: no agent should ever benefit from misrepresenting their preferences. We show that no such rule exists. A variety of domains have been explored and similar negative results have been proved but one would have hoped that the domain of linear preferences is sufficiently narrow to allow for some positive results. Our result dashes such hopes.

This is a survey of the literature of (approximately) the last 10 years on the axiomatic approach to conflict resolution formulated by Nash (Econometrica 28:155–162, 1950). It updates two previous surveys (Thomson, in: Aumann, Hart (eds) Handbook of game theory, North-Holland, 1994, in: Thomson (ed) Bargaining and the theory of cooperative games: John Nash and beyond, Edward Elgar Publishing Ltd, Camberly, Northampton, 2010).