Individual rationality

Perception of risk in adults is usually described, or interpreted, with reference to health belief models (HBMs) (Ajzen and Fishbein, 1980 Janz and Becker, 1984). Individuals are more likely to engage in health behaviors if they perceive vulnerability to health threats that the consequences are severe that treatment or preventive measures will be successful. Although there are variants to the framework, the different models share many of the same elements. In effect, theories assume that individuals rationally weigh benefits and costs and act according to the outcome of this analysis. Subsequent modifications to the models include the addition of perceived social or monetary barriers to the adaptive response. A cue to action which can be internal (e.g., symptoms) or external (e.g., health communication) is hypothesized to trigger these... 

For Marx, counterfinality the negative externalities of the capitalist mode of production was a more interesting phenomenon. He believed that capitalism systematically tends to aggravate spontaneously arising crises, since each entrepreneur reacts to them by behaviour that, even if individually rational, is disastrous in the aggregate. The main instance of this mechanism Marx found in the process that according to him tends to... 

To keep matters simple, restrict the focus to two time periods. (Since next period s payoff could represent the then present expected value of all subsequent payoffs, the problem is not qualitatively altered.) For labor s retaliation to be individually rational, the following condition must hold ... 

Correspondingly, management finds it individually rational to introduce or maintain an occupational risk if... 

Gode, D., Sunder, S. Allocative efficiency of markets with zero-intelligence traders markets as a partial substitute for individual rationality. J. Poht. Econ. 101(1), 119-137 (1993)... 

In bilateral bargaining with complete information (Figure 3.1-(a)), the supplier s opportunity cost is s and the buyer s willingness to pay is V. The intermediary determines if the trade is to take place (/ ) based on the cost information. If so, she collects asked price p from the buyer and pay bid price w to the supplier. The intermediary determines / ,p, w to maximize a certain function subject to individual rationality (see Section... 

In other words, there is no incentive for the players to report v and s when their true valuations are v and s, respectively. The mechanism is said to be individually rational if it offers each player an expected gain that is non-zero. 

Thus, f (l G(T))F(r)dT is the minimum subsidy required from the intermediary. However, a profit-minded intermediary may want to optimize her profit over a longer time horizon, or design a trading mechanism that would maximize her profit in each individual trade. The former requires enhanced knowledge of the market which presents an interesting research topic to be discussed further. The latter could be done by a mechanism which only allow profitable (while individually rational) trades to take place. We describe the construct of such a mechanism in the following. 

Based on the supply chain intermediation framework outlined above, the intermediary devises a direct mechanism T P p,w) to maximize her profit (3.35), subject to incentive compatibility and individual rationality. First, the intermediary must determine P s, v) which specifies whether the trade is to take place given the reported s, v and her knowledge of their virtual opportunity costs and virtual willingness to pay. Given the simple form of the profit function (3.35) it is straightforward to find a profit maximizing P subject to individual rationality as follows ... 

Theorem 3 Suppose ft(.) and 5(.) are monotone increasing functions in [vi V2] and [51,52], respectively. Then among all individually rational mechanisms, the intermediary s expected profit is maximized by a mechanism in which the trade takes place iff i v) > s(5). 

Similar to the bilateral case, the intermediary could satisfy the individual rationality constraint by offering no additional surplus to the players, i.e.,... 

IR) individual-rationality. An agent s expected payoff is greater than its payoff from non-participation. 

The uniqueness of Groves mechanisms provides an additional simplification to the efficient mechanism design problem when dominant strategy implementations are required. It is sufficient to consider the family of Groves mechanisms, and look for functions hi -) that provide Groves payments that satisfy all of the desired constraints. The Vickrey-Clarke-Groves (VCG) mechanism is an important special case, so named because it reflects the seminal ideas due to Vickrey [100] and Clarke [26]. The VCG mechanism maximizes expected revenue across all strategyproof efficient mechanisms, subject to ex post individual-rationality (IR) constraints. Ex post IR provides ... 

The (IR ) constraints ensure that truthful bids and asks are (ex post) individual-rational for an agent, such that an agent has non-negative utility for participation whatever the bids and asks received by the exchange. Constraints (VD) ensure that no agent receives more than its Vickrey discount. The authors consider a variety of distance functions, including standard metrics such as 2( 5 vick) (Ayick.2 Aj) and Lqo(A, Ayick) 2) ... 

This constraint is called individual rationality (IR). If we add a dummy type, to which assigns utility 0 to all allocations, and set Pq = 0, we can fold the IR constraint into the IC constraint. So, from now on T contains the dummy type to. 

Now, amongst all auctions that produce the efficient allocation, are ex-post individually rational, in which bidding truthfully is a dominant strategy, which one maximizes the revenue of the auctioneer The answer to this question was provided by Groves [35] and Clarke [16] with the impetus coming from Vickrey s seminal 1961 paper [66]. For this reason the auction is called the Vickrey-Clarke-Groves mechanism or VCG for short. We show how to derive it using the ideas described above. 

Suppose you face severe complementarities amongst the bidders and your goal is to reduce the payments made by you to them. Is there another auction that is incentive compatible and individually rational that one might use ... 

It is sometimes common to require that the actual payoff be non-negative rather than the expected payoff as we have done here. This stronger condition is called ex-post individual rationality. 

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