Why DeDeal Works

Intro

When DeDeal is modeled using "A SIMPLE MODEL OF INEQUITY AVERSION" from the research paper referenced below, we can show that fraud does not occur between players with tendencies of "inequity aversion."

“Inequity aversion" is the tendency to resist unfair outcomes (i.e. they are willing to forego some material rewards in order to obtain a fairer outcome).

There is substantial evidence to suggest that "inequity aversion" influences the behavior of many people, seen through the results of both economic experiments such as the ultimatum game and real-world empirical results in corporate wage setting.

ReferenceFehr, Ernst, and Klaus M. Schmidt. “A Theory of Fairness, Competition, and Cooperation.” The Quarterly Journal of Economics, vol. 114, no. 3, 1999, pp. 817–68. JSTOR.

Modeling

General Model

“A SIMPLE MODEL OF INEQUITY AVERSION” for players i and j is as follows

Ui(x)=xiαi×max(xjxi,0)βi×max(xixj,0),ijU_i(x) = x_i - \alpha_i \times \max(x_j - x_i, 0) - \beta_i \times \max(x_i - x_j, 0), i \ne j

Ui(x)U_i(x) : Player i's utility function

xix_i: Player i's monetary utility

xjx_j : Player j's monetary utility

αi\alpha_i: Player i's utility loss multiplier due to inequality against their favor

βi\beta_i: Player i's utility loss multiplier due to inequality in their favor

Seller fraud pattern

Applying this model to the situation where the seller commits fraud and fails to ship the item at price P, the options for the buyer and seller are as follows

・Phase 0

Choice of whether or not the seller commits fraud

・Phase 1

Choice of whether or not the buyer presses the sanction button in the case of fraudulent non-shipment of item by the seller

Ub(P)U_b(P): Buyer's utility function

PP: Price of the product

xbx_b: Buyer's monetary utility

xsx_s: Seller's monetary utility

αbα_b: Buyer's utility loss multiplier due to inequality against their favor

βbβ_b: Buyer's utility loss multiplier due to inequality in his favor

RbR_b: Buyer's utility loss due to the risk that the buyer deposit to press the sanction button is lost due to the seller sanctioning back

<Option 1-1>

Buyer's utility function if the buyer does not press the sanction button:

<Option 1-2>

Buyer's utility function if the buyer presses the sanction button:

Ub(P)=Pαb×(0)βb×(0)Rb=PRbU_b(P) = -P - \alpha_b \times (0) - \beta_b \times (0) - R_b = -P - R_b

(RbRb is 2P2P if the seller presses the sanction button in Phase 2 and 00 if not.)

・Phase 2

Choice of whether or not the seller presses the sanction button when the buyer chooses to sanction

Us(P)U_s(P): Seller's utility function

PP: Price of the item

xsx_s: Seller's monetary utility

xbx_b: Buyer's monetary utility

αsα_s: Seller's utility loss multiplier due to inequality against their favor

βsβ_s: Seller's utility loss multiplier due to inequality in their favor (this value is 00 because the seller is committing fraud)

<Option 2-1>

Seller's utility function if the seller does not press the sanction button:

Us(P)=Pαs×(0)βs×(0)U_s(P) = -P - \alpha_s \times (0) - \beta_s \times (0)

<Option 2-2>

Seller's utility function if the seller presses the sanction button:

Us(P)=Pαs×(0)0×(P(3P))Rs=PRsU_s(P) = -P - \alpha_s \times (0) - 0 \times (-P - (-3P)) - R_s = -P - R_s

(RsRs is 2P2P if the buyer sanctions back afterwards and 00 if not)

Now, assuming that the buyer chooses <Option 2> in phase 1, we can expect that in phase 2 the seller will compare the Us(P)U_s(P) values associated with <options 2-1> and <options 2-2> and opt for option 3.

If <Option 2-1> is chosen in Phase 2, then since "Rb" is 0 in Phase 1, we can expect the buyer to compare the values of Ub(P) when choosing <Option 1-1> and <Option 1-2>, and choose <Option 1-2>.

In other words, if the seller chooses to commit fraud in Phase 0, the expected final utility of each option is as follows, which means that if the buyer is an "inequity aversive" player, the seller should not commit fraud.

Us(P)=PU_s(P)=-P

Ub(P)=PU_b(P)=-P

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