Pairwise Exchanges of Freely Replicable Goods with Negative Externalities

Abstract

We study a setting where a set of agents engage in pairwise exchanges of freely replicable goods (e.g., digital goods such as data), where two agents grant each other a copy of a good they possess in exchange for a good they lack. Such exchanges introduce a fundamental tension: while agents benefit from acquiring additional goods, they incur negative externalities when others do the same. This dynamic typically arises in real-world scenarios where competing entities may benefit from selective collaboration. For example, in a data sharing consortium, pharmaceutical companies might share (copies of) drug discovery data, when the value of accessing a competitor's data outweighs the risk of revealing their own. In our model, an altruistic central planner wishes to design an exchange protocol (without money), to structure such exchanges between agents. The protocol operates over multiple rounds, proposing sets of pairwise exchanges in each round, which agents may accept or reject. We formulate three key desiderata for such a protocol: (i) individual rationality: agents should not be worse off by participating in the protocol; (ii) incentive-compatibility: agents should be incentivized to share as much as possible by accepting all exchange proposals by the planner; (iii) stability: there should be no further mutually beneficial exchanges upon termination. We design an exchange protocol for the planner that satisfies all three desiderata. While the above desiderata are inspired by classical models for exchange, free-replicability and negative externalities necessitate novel and nontrivial reformalizations of these goals. We also argue that achieving Pareto-efficient agent utilities -- often a central goal in exchange models without externalities -- may be ill-suited in this setting.

Figures (8)

• Figure 1: Agent $i$ holds goods 1,3, and 4, while $j$ holds goods 2 and 3. In a pairwise exchange, $i$ could give good 1 to $j$ and receive good 2. Both agents then retain all previously held goods and also acquire the newly received good.
• Figure 2: Agent $k$ holds both goods, while $i$ and $j$ hold only one each.
• Figure 3: (\ref{['fig:naivesub']}) There are 4 agents and 3 goods with $x^{(0)}_i = [1, 0, 0]$, $x^{(0)}_j = [0, 1, 0]$, and $x^{(0)}_k = x^{(0)}_l = [0, 0, 1]$. In round 1, the protocol proposes three exchanges $P_1 = \{((i, 1), (j, 2)), ((i, 1), (k, 3)), ((j, 2), (k, 3))\}$; if all are accepted, it results in a stable allocation. However, suppose $((i, 1), (k, 3))$ was rejected by either agent. In round 2, the protocol proposes $P_2 = \{((i, 1), (l, 3))\}$. If accepted, this results in the stable allocation shown. Recall, we disallow agents from onward-sharing goods they received from others in exchange for more goods. (\ref{['fig:notnicsub']}) Consider 3 agents $i, j, k$ and initial goods $x^{(0)}_i = [1, 0, 1]$, $x^{(0)}_j = [0, 1, 0]$, $x^{(0)}_k = [1, 0, 0]$. Suppose the protocol proposes $P_1 = \{((i, 1), (j, 2))\}$, which results in a stable allocation if accepted. However, agent $j$ may reject it, as she would gain only one additional good in the final allocation. In particular, she may hope to get (the rarer) good 3 from $i$ and good 1 from $k$, for a total of two goods. However, had the protocol instead proposed $P_1 = \{((i, 3), (j, 2)), ((j, 2), (k, 1))\}$, then $j$ will accept both proposals since she gains two goods. Similarly, $k$ will accept her proposal as she gains a good, and $i$ will also accept (provided that both $j$ and $k$ follow the accepting policy), since rejecting it would result in not receiving good 2.
• Figure 4: An instance illustrating the challenges in IR.
• Figure 5: Illustration of our graph construction in the IR proof on two instances (a) and (b). In both instances, we have 4 goods and 4 agents $\{i,j,k,l\}$ with $\beta_{ij} < \beta_{ik} < \beta_{il} < \beta_{jk} < \beta_{jl} < \beta_{kl}$. A shaded square means the agent originally has that good; for instance, in (\ref{['fig:IRsub1-intro']}), agent $i$'s initial allocation is $x^{(0)}_i = [1, 0, 1, 0]$. Each agent-good pair is a vertex. Edges represent exchanges; for instance, the edge between $(i, 2)$ and $(j, 1)$ in (\ref{['fig:IRsub1-intro']}) represents the exchange $((i, 1), (j, 2))$ where $i$receives a copy of good $2$ from $j$, while $j$ receives $1$. In instance (\ref{['fig:IRsub1-intro']}), if $i$ participates, CLEAR would propose $E = \{\{(i, 2), (j, 1)\}, \{(i, 4), (j, 3)\}, \{(k, 2), (l, 1)\}\}$. If $i$ does not participate, CLEAR would propose $E' = \{\{(j, 1), (k, 2)\}, \{(j, 3), (k, 4)\}\}$. Edges only in $E$ are red, edges only in $E'$ are blue, and edges in both are green. The paths which have alternating red and blue edges are tracked paths.

Theorems & Definitions (29)

• Theorem 1: Informal
• Theorem 2: Informal
• Theorem 3: Informal
• Theorem 4: Informal
• Theorem 5: Informal
• Theorem 5
• Theorem 5
• Remark 1
• Theorem 5
• Lemma 1: Informal