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Iterated crowdsourcing dilemma game.

Oishi K, Cebrian M, Abeliuk A, Masuda N - Sci Rep (2014)

Bottom Line: We enumerate pure evolutionarily stable strategies within the class of so-called reactive strategies, i.e., those depending on the last action of the opponent.Among the 4096 possible reactive strategies, we find 16 strategies each of which is stable in some parameter regions.Under the current framework, repeated interactions do not really ameliorate the crowdsourcing dilemma in a majority of the parameter space.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan [2] CREST, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.

ABSTRACT
The Internet has enabled the emergence of collective problem solving, also known as crowdsourcing, as a viable option for solving complex tasks. However, the openness of crowdsourcing presents a challenge because solutions obtained by it can be sabotaged, stolen, and manipulated at a low cost for the attacker. We extend a previously proposed crowdsourcing dilemma game to an iterated game to address this question. We enumerate pure evolutionarily stable strategies within the class of so-called reactive strategies, i.e., those depending on the last action of the opponent. Among the 4096 possible reactive strategies, we find 16 strategies each of which is stable in some parameter regions. Repeated encounters of the players can improve social welfare when the damage inflicted by an attack and the cost of attack are both small. Under the current framework, repeated interactions do not really ameliorate the crowdsourcing dilemma in a majority of the parameter space.

No MeSH data available.


Related in: MedlinePlus

Details of region (A).(a) Three subregions of region (A) in the (d, q) space. (b), (c), (d) Relative sizes of the attractive basins. (b) uncond-CA, (c) strategy 12, and (d) strategy 14. We set . The two solid lines in (b), (c), and (d) represent the boundaries between the subregions. The size of attractive basin of strategies 12 and 14 is equal to zero in region (L2) and region (K), respectively, because they are not ESSs in the corresponding region.
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f4: Details of region (A).(a) Three subregions of region (A) in the (d, q) space. (b), (c), (d) Relative sizes of the attractive basins. (b) uncond-CA, (c) strategy 12, and (d) strategy 14. We set . The two solid lines in (b), (c), and (d) represent the boundaries between the subregions. The size of attractive basin of strategies 12 and 14 is equal to zero in region (L2) and region (K), respectively, because they are not ESSs in the corresponding region.

Mentions: In the previous section, we revealed that conditional strategies were the only efficient ESSs in region (A). For these conditional strategies to establish a foothold in an evolutionary context, they should also have a sufficiently large attractive basin under evolutionary dynamics. Therefore, we compare the relative size of the attractive basins of the ESSs in region (A). We examine replicator dynamics composed only of ESSs because it is not feasible to treat the dynamics composed of all 4096 strategies. Region (K) allows two ESSs, i.e., uncond-CA and strategy 12. Region (L) is divided into subregion (L1) that allows three ESSs, i.e., uncond-CA, strategy 12, and strategy 14, and subregion (L2) that allows two ESSs, i.e., uncond-CA and strategy 14. The boundary between (L1) and (L2) is given by q = 1 − 2d. These regions within region (A) are depicted in Figure 4(a). We separately calculated the size of attractive basins for regions (K), (L1), and (L2).


Iterated crowdsourcing dilemma game.

Oishi K, Cebrian M, Abeliuk A, Masuda N - Sci Rep (2014)

Details of region (A).(a) Three subregions of region (A) in the (d, q) space. (b), (c), (d) Relative sizes of the attractive basins. (b) uncond-CA, (c) strategy 12, and (d) strategy 14. We set . The two solid lines in (b), (c), and (d) represent the boundaries between the subregions. The size of attractive basin of strategies 12 and 14 is equal to zero in region (L2) and region (K), respectively, because they are not ESSs in the corresponding region.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3924214&req=5

f4: Details of region (A).(a) Three subregions of region (A) in the (d, q) space. (b), (c), (d) Relative sizes of the attractive basins. (b) uncond-CA, (c) strategy 12, and (d) strategy 14. We set . The two solid lines in (b), (c), and (d) represent the boundaries between the subregions. The size of attractive basin of strategies 12 and 14 is equal to zero in region (L2) and region (K), respectively, because they are not ESSs in the corresponding region.
Mentions: In the previous section, we revealed that conditional strategies were the only efficient ESSs in region (A). For these conditional strategies to establish a foothold in an evolutionary context, they should also have a sufficiently large attractive basin under evolutionary dynamics. Therefore, we compare the relative size of the attractive basins of the ESSs in region (A). We examine replicator dynamics composed only of ESSs because it is not feasible to treat the dynamics composed of all 4096 strategies. Region (K) allows two ESSs, i.e., uncond-CA and strategy 12. Region (L) is divided into subregion (L1) that allows three ESSs, i.e., uncond-CA, strategy 12, and strategy 14, and subregion (L2) that allows two ESSs, i.e., uncond-CA and strategy 14. The boundary between (L1) and (L2) is given by q = 1 − 2d. These regions within region (A) are depicted in Figure 4(a). We separately calculated the size of attractive basins for regions (K), (L1), and (L2).

Bottom Line: We enumerate pure evolutionarily stable strategies within the class of so-called reactive strategies, i.e., those depending on the last action of the opponent.Among the 4096 possible reactive strategies, we find 16 strategies each of which is stable in some parameter regions.Under the current framework, repeated interactions do not really ameliorate the crowdsourcing dilemma in a majority of the parameter space.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan [2] CREST, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.

ABSTRACT
The Internet has enabled the emergence of collective problem solving, also known as crowdsourcing, as a viable option for solving complex tasks. However, the openness of crowdsourcing presents a challenge because solutions obtained by it can be sabotaged, stolen, and manipulated at a low cost for the attacker. We extend a previously proposed crowdsourcing dilemma game to an iterated game to address this question. We enumerate pure evolutionarily stable strategies within the class of so-called reactive strategies, i.e., those depending on the last action of the opponent. Among the 4096 possible reactive strategies, we find 16 strategies each of which is stable in some parameter regions. Repeated encounters of the players can improve social welfare when the damage inflicted by an attack and the cost of attack are both small. Under the current framework, repeated interactions do not really ameliorate the crowdsourcing dilemma in a majority of the parameter space.

No MeSH data available.


Related in: MedlinePlus