Strategic Non-Shareability

• Strategic non-shareability is a phenomenon where technically shareable objects are selectively withheld due to equilibrium incentives, institutional constraints, or resource limits.
• It spans applications from GenAI content sharing and network public goods to oligopolies and quantum games, influencing both information flow and competitive behavior.
• Research employs models like Nash equilibria, mechanism design, and quantum anti-collusion to reveal non-intuitive effects of increased transferability on efficiency and market dynamics.

Searching arXiv for papers directly related to “strategic non-shareability” and adjacent formulations in sharing, disclosure, and information-sharing games. arXiv search query: "strategic non-shareability sharing disclosure competition information sharing"

Strategic non-shareability denotes a class of strategic environments in which an object is technically shareable, but equilibrium incentives, institutional constraints, or resource-theoretic limits make withholding, selective sharing, non-disclosure, or non-extendability central to the outcome. The object being shared varies across models: content for a platform’s GenAI, public goods on a network, private signals in oligopoly, product information in sharing markets, inferred decision rules in strategic learning, covert communication capacity in confinement, and bipartite correlations in quantum-mediated games. Across these settings, the recurring issue is that sharing can increase aggregate informational or productive value while simultaneously exposing the sharer to exploitation, intensified competition, collusion, or free-riding (Keinan et al., 22 May 2025, Gerke et al., 2019, Wang, 25 May 2026).

1. Formal scope of the concept

In the GenAI platform model of "Strategic Content Creation in the Age of GenAI: To Share or Not to Share?", creators make dual strategic decisions: investment in content quality and possible consent to share their content with the platform’s GenAI. The platform, in turn, strategically allocates a portion of its GenAI-driven revenue to creators who share their content, and the analysis focuses on full-sharing equilibrium profiles in which all creators willingly share (Keinan et al., 22 May 2025).

In "Public goods in networks with constraints on sharing", strategic non-shareability is encoded as a constrained nomination decision. Each player chooses a contribution $x_i$ and a nomination set $S_i \subseteq N_G(i)$ of fixed size $\kappa(i)$, with payoff

$$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$

Here, the strategic choice is not only how much to provide, but whom to exclude from consumption (Gerke et al., 2019).

In oligopoly information sharing, the central object is the participation gain

$$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$

with the participation constraint $\Delta_i(m)\ge 0$. Non-shareability appears when disclosure is privately unprofitable even though the pooled statistic has decision value (Liu et al., 1 Jun 2026). In sharing markets, sellers choose disclosure levels $\sigma_i\in[0,1]$ and prices $p_i$; in that framework, full disclosure and non-disclosure are both strategic outcomes shaped by competition (Ding et al., 2023). In quantum-mediated private-information games, the notion is formalized geometrically as the distance from an authorized behavior to the set of behaviors a colluder can reproduce while preserving the authorized marginal (Wang, 25 May 2026).

These formulations differ in primitives, but they share a common structural feature: the act of sharing changes both the informational environment and the strategic environment. This suggests that non-shareability is not merely the absence of transferability; it is an equilibrium property of environments in which disclosure reshapes rivals’ or outsiders’ feasible responses.

2. Network public goods and selective exclusion

The network model of constrained sharing studies a finite undirected graph $G=(N,E)$ in which each player chooses both a contribution and a subset of neighbors to nominate as co-beneficiaries. The nomination set has fixed size $\kappa(i)$, saturating at $S_i \subseteq N_G(i)$0 when $S_i \subseteq N_G(i)$1. A player’s benefit depends on own contribution plus any contribution from neighbors who nominate that player, while the cost is private and linear in own provision (Gerke et al., 2019).

A central equilibrium concept is the specialised pure-strategy Nash equilibrium, in which each $S_i \subseteq N_G(i)$2. The set $S_i \subseteq N_G(i)$3 are providers and $S_i \subseteq N_G(i)$4 are free-riders. In any such equilibrium, providers exactly exhaust their sharing capacity, and none of those neighbors nominate them; otherwise a provider would receive free access and prefer $S_i \subseteq N_G(i)$5. Free-riders, conversely, must be nominated by at least one provider so that remaining at zero is optimal. Graph-theoretically, the equilibrium structure is represented by a spanning bipartite subgraph $S_i \subseteq N_G(i)$6 with partite sets $S_i \subseteq N_G(i)$7, where each provider has degree exactly $S_i \subseteq N_G(i)$8 and each free-rider degree at least $S_i \subseteq N_G(i)$9. The existence of such a DP-Nash subgraph is equivalent to the existence of a specialised equilibrium (Gerke et al., 2019).

The paper proves that for any network $\kappa(i)$0 and capacity function $\kappa(i)$1, the game admits at least one specialised pure-strategy Nash equilibrium. It also defines efficiency among specialised equilibria in terms of the number of providers $\kappa(i)$2: efficient equilibria minimize $\kappa(i)$3, while inefficient equilibria maximize it. The comparative statics are non-monotone. When capacities are raised from $\kappa(i)$4 to $\kappa(i)$5 with $\kappa(i)$6 for all $\kappa(i)$7, the smallest-provider equilibrium under more generous sharing is no worse than the largest-provider equilibrium under tighter sharing, but an increase in shareability may nevertheless decrease efficiency. The six-node double-star example shows that increasing $\kappa(i)$8 from $\kappa(i)$9 to $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$0 on the two central nodes can raise the minimal equilibrium provider set from size $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$1 to size $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$2 (Gerke et al., 2019).

The strategic significance is explicit: providers choose whom to exclude in order to deter free-riding. Limited shareability can therefore improve or worsen welfare depending on network structure. This directly contradicts the monotonic intuition that more transferability must increase efficiency.

3. Competition, disclosure, and endogenous non-participation

In "Privacy-preserving Information Sharing in Oligopoly Competitions", $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$3 firms compete à la Cournot under uncertain demand $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$4, observe private Gaussian signals $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$5, and may submit privatized reports $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$6 to a platform. The platform aggregates reports and an optional external signal $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$7 into the posterior mean $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$8. In a two-firm market without an external signal, firms refuse to share regardless of the privacy level: for all privacy noise levels $$u_i(x,S)=f\Bigl(x_i+\sum_{j: i\in S_j}x_j\Bigr)-c\,x_i.$$9, $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$0. More generally, privacy protection alone is insufficient to incentivize disclosure; it must be combined with a sufficiently informative external signal. In larger $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$1-firm markets, sharing may arise even without privacy safeguards because a non-participating firm loses access to the aggregated signal, creating an access-loss penalty. The paper also shows that firms with more accurate private signals require stronger privacy protection, formalized by $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$2 (Liu et al., 1 Jun 2026).

In "Information Disclosure under Competition in Sharing Systems", sellers choose disclosure levels and prices in a two-stage game. The paper shows that full disclosure by all sellers or non-disclosure by all sellers will both lead to intense price competition. The all-disclosure case is never an equilibrium even when all sellers have good commodity qualities and low privacy costs, whereas the all-non-disclosure case can be an equilibrium under which all sellers get zero profit. Capacity limitations and buyers’ estimation biases encourage information disclosure because they mitigate sellers’ competition (Ding et al., 2023).

In "Strategic Data Sharing between Competitors", the object of sharing is training data. Firms compete in a duopoly with inverse demand $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$3, while expected marginal cost follows

$$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$4

The paper derives break-even thresholds for full sharing and shows that reduced competition, in terms of the similarities between the firms’ products, and harder learning tasks foster collaboration. Formally, the critical threshold is increasing in $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$5 and in $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$6, so higher product substitutability and easier tasks make sharing less attractive. In the partial-sharing Nash-bargaining solution, the smaller-data firm always shares everything, while the larger-data firm’s optimal share decreases in both $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$7 and $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$8 (Tsoy et al., 2023).

Taken together, these results identify a common market mechanism behind strategic non-shareability: disclosure improves information quality or buyer matching, but also hardens competition. Whether sharing survives depends on the relative strength of the informational gain, the strategic exposure, and any institutional feature—such as access conditionality, privacy noise, external information, or capacity constraints—that changes that balance.

4. Platform incentives, audits, and implementability

The GenAI platform model makes strategic non-shareability a mechanism-design problem internal to the platform-creator relationship. Creators choose both quality investment and whether to share their content with the platform’s GenAI, while the platform allocates part of GenAI-driven revenue to sharers. The paper’s main technical contribution is an optimization problem that approximates the platform’s optimal revenue subject to inducing a full-sharing equilibrium. It identifies conditions under which full-sharing equilibria exist and reports a surprising connection to the Prisoner’s Dilemma. Simulations then show how revenue-allocation mechanisms affect creator utility and platform revenue (Keinan et al., 22 May 2025).

A distinct mechanism-design response appears in "Sharing with Frictions: Limited Transfers and Costly Inspections". There, an incumbent $$\Delta_i(m)=\mathbb E[\pi_i^S(m)]-\mathbb E[\pi_i^{NS}],$$9 and a commercial user $\Delta_i(m)\ge 0$0 have private types $\Delta_i(m)\ge 0$1 and $\Delta_i(m)\ge 0$2, exclusivity is represented by $\Delta_i(m)\ge 0$3, inspection by $\Delta_i(m)\ge 0$4, and the entry fee by $\Delta_i(m)\ge 0$5. The planner maximizes expected welfare subject to incentive-compatibility, budget-balance, and feasibility constraints. The optimal mechanism is deterministic, threshold-based, and characterized by cutoffs in $\Delta_i(m)\ge 0$6 for each $\Delta_i(m)\ge 0$7. The paper identifies three regimes: $\Delta_i(m)\ge 0$8 implies default exclusivity and no inspection; $\Delta_i(m)\ge 0$9 implies targeted inspection; and $\sigma_i\in[0,1]$0 implies automatic sharing with no audit. Strategic non-shareability arises because the incumbent privately exaggerates interference to block sharing. Costly inspection disciplines over-reporting and restores truth-telling, while the resulting second-best allocation approaches the first best as $\sigma_i\in[0,1]$1 (Bobbio et al., 25 Dec 2025).

These two papers locate non-shareability inside the design of institutions rather than treating it as an immutable preference. One mechanism uses revenue allocation to make sharing privately attractive; the other uses audit technology and entry fees to screen strategic obstruction. This suggests that non-shareability can often be shifted, but not eliminated, by redesigning payoffs and verification.

5. Hidden rules, information discrepancy, and strategic confinement

In "Information Discrepancy in Strategic Learning", the relevant object is not a good or a signal but knowledge of the principal’s decision rule. The principal chooses a hidden linear rule $\sigma_i\in[0,1]$2, while agents in group $\sigma_i\in[0,1]$3 infer only

$\sigma_i\in[0,1]$4

from peer data, where $\sigma_i\in[0,1]$5 is the projection onto the support subspace of that group’s feature distribution. Given quadratic modification costs, an agent’s best response is

$\sigma_i\in[0,1]$6

The paper shows that even the welfare-optimal rule may generate a strong negative externality: the true quality of some groups can deteriorate. It also gives conditions under which simultaneous improvement for all groups is guaranteed, introduces the information overlap proxy

$\sigma_i\in[0,1]$7

and shows that under identical costs this proxy upper-bounds disparity in improvements across groups (Bechavod et al., 2021).

"A Note on the Strategic Confinement Problem" generalizes the logic of non-shareability from market design to covert communication. Classical confinement bounds the information leakage $\sigma_i\in[0,1]$8. Strategic confinement instead asks for the maximum worst-case damage

$\sigma_i\in[0,1]$9

that strategic sender and receiver can realize by using residual channel capacity $p_i$0 to signal a low-entropy, high-impact predicate of confidential data. The paper’s core claim is that negligible capacity need not imply negligible harm: a channel with negligible capacity may still suffice to select damaging outcomes. The argument relies on strategic agents’ ability to coordinate on a damaging predicate and concentrate communication on that predicate rather than on the full secret. The paper further argues that systems of learnt strategic agents naturally instantiate this problem because they do not admit complete behavioural specifications, their learnt conventions are difficult for an external observer to predict or reproduce, and sufficiently capable agents can construct covert communication schemes that are difficult to detect or eliminate (Witt, 7 Jun 2026).

In both papers, non-shareability is tied to asymmetry in who can infer or reconstruct the strategically relevant object. One concerns asymmetric access to the decision rule; the other concerns asymmetric ability to coordinate on covert encodings. In each case, low transparency does not merely reduce information flow; it redistributes strategic power.

6. Quantum anti-collusion and cross-cutting implications

In "Strategic Non-Shareability of Quantum Correlations", the problem is whether coordination distributed to an authorized pair can be inherited by a colluder without disturbing the authorized marginal. For a fixed authorized behavior $p_i$1, the paper defines the collusive shadow

$p_i$2

and then defines strategic non-shareability as the total-variation distance to this shadow,

$p_i$3

Its main theorem states that, on finite alphabets, the game-optimized anti-collusion capacity equals this distance. In the CHSH score slice, Toner–Verstraete monogamy yields the exact certified frontier: $p_i$4 The Bell local bound $p_i$5 is the sharp onset of positive certified anti-collusion power, the value saturates at $p_i$6 for the maximally entangled CHSH strategy, and classical hidden-variable mediators have zero capacity in this slice. The paper also gives a Hoeffding-based finite-data certification protocol and a level-2 NPA semidefinite relaxation for tilted Bell inequalities (Wang, 25 May 2026).

Several recurring misconceptions are directly contradicted by the literature. More shareability does not necessarily improve efficiency: in network public goods, an increase in shareability may decrease efficiency (Gerke et al., 2019). Privacy protection alone does not necessarily induce voluntary sharing: in Cournot oligopoly, it must be combined with a sufficiently informative external signal (Liu et al., 1 Jun 2026). Full transparency is not generically stable: in sharing systems, full disclosure by all sellers is never an equilibrium (Ding et al., 2023). Low leakage capacity does not imply low harm: strategic confinement shows that tiny channels can still support maximal damage when agents coordinate on low-entropy predicates (Witt, 7 Jun 2026). And in the quantum setting, the central issue is not whether correlations exist, but whether they admit collusive extensions preserving the authorized marginal (Wang, 25 May 2026).

These results suggest a broad encyclopedia-level characterization. Strategic non-shareability is not a single theorem or a single application domain. It is a recurring game-theoretic pattern in which the value of a shared object is inseparable from the strategic consequences of making it replicable, inferable, or accessible. In some models the object is selectively withheld; in others it is never voluntarily disclosed; in still others it cannot be losslessly extended at all. What unifies the literature is the shift from asking whether sharing is technologically feasible to asking whether sharing is strategically supportable.