Exploring the interaction and choice behavior of organization and individuals in the crowd logistics

Abstract

With the increasingly wide use of sensor-embedded smartphones, we envision that there will be many crowdsourced logistic companies to acquire logistics service from a large population of carriers. They form a two-side competition market, where crowdsources compete for the limited logistics service and carriers compete for the compensation from crowdsourced logistic company. Each crowdsourced logistic company has to select an “optimal” delivery compensation that can attract enough service providers. Each carrier has to decide which crowdsourced logistic company to join in, while a congested company may resulted in a low reward. In this paper, we present a game theoretic study of such a two-side competition market. To be more practical, we consider the bounded rationality of service providers. We formulate the dynamics behavior of service providers as an evolutionary game, and take two key factors (company’s analytics ability and service providers’ evaluation) under smart environment in our model, and then present a simulation model for the implementation of evolution process. Through this work, we can understand the dynamic evolution of the medium-sized crowd logistics market under smart environment and crowdsourced logistic company can adjust their strategy to optimal their profit.

Appendices

Appendix 1

We give an example to express the replicator dynamics in evolutionary smartphone competition game, where the number of crowdsourced logistic company M = 2. The number of service providers can be any real number, since what really matters is the proportion of service providers choosing different crowdsourced logistic company. We name the two crowdsourced logistic company as Crowdsourced logistic company-A and Crowdsourced logistic company-B respectively.

At time t, each service provider randomly chooses a crowdsourced logistic company, resulting in a strategy proportion $\left\{ {x_{1} \left( t \right),x_{2} \left( t \right)} \right\}$. Service providers selecting Crowdsourced logistic company-A and Crowdsourced logistic company-B reveice payoffs $p_{1} \left( s \right) - c$ and $p_{2} \left( s \right) - c$.

Each service provider compares its payoff with the average system payoff

$$ \overline{p} \left( s \right) - c = \frac{{p_{1} \left( s \right) \cdot x_{1} \left( t \right) \cdot N\left( t \right) + p_{2} \left( s \right) \cdot x_{2} \left( t \right) \cdot N\left( t \right)}}{N\left( t \right)} - c = p_{1} \left( s \right) \cdot x_{1} \left( t \right) + p_{2} \left( s \right) \cdot x_{2} \left( t \right) - c. $$

(8)

If $p_{1} \left( s \right) < \overline{p} \left( s \right)$, service providers with strategy Crowdsourced logistic company-B stick to Crowdsourced logistic company-B in the next time slot.

The proportion of service providers with strategy Crowdsourced logistic company-A switching to Crowdsourced logistic company-B in the next time slot is y₂(t) of the population, as Eq. (9) calculates

$$ \left( {p_{2} \left( s \right) - \overline{p} \left( s \right)} \right)N\left( t \right)x_{2} \left( t \right) = \overline{p} \left( s \right)N\left( t \right)y_{2} \left( t \right) $$

(9)

Solving Eq., we have

$$ y_{2} \left( t \right) = \left( {\frac{{p_{2} \left( s \right)}}{{\overline{p} \left( s \right)}} - 1} \right) \cdot x_{2} \left( t \right) $$

(10)

The left part of Eq. (9) indicates the amount of payoffs to spare in crowdsourced logistic company joining Crowdsourced logistic company-B, while the right part shows the additional number of satisfied service providers that Crowdsourced logistic company-B can manage. Negative value of the right part is also reasonable, which means that the number of service providers joining a over-congested crowdsourced logistic company (i.e., payment of each provider lower than the average level) needs to be reduced.

Appendix 2

During communications, individuals exchange opinions containing the value of state variables. The opinion and its uncertainty are modified during communications according to the relative agreement model (Deffuant et al., 2002).

It considered a population of $N$ Agent, each agent i is characterised by two variables, its opinion $x_{i}$ and its uncertainty $u_{i}$, and the opinion segments are $\left[ {x_{i} - u_{i} ,x_{i} + u_{i} } \right]$, $h_{ij}$ is defined as the opinion overlap of agent i and agent j.

$$ h_{ij} = \min \left( {x_{i} + u_{i} ,x_{j} + u_{j} } \right) - \max \left( {x_{i} - u_{i} ,x_{j} - u_{j} } \right) $$

(11)

If $h_{ij} > u_{i}$, then the modification of $x_{j}$ and $u_{j}$ by the interaction with i is:

$$ x_{j} = x_{j} + \mu \cdot \left( {\frac{{h_{ij} }}{{u_{i} }} - 1} \right) \cdot \left( {x_{i} - x_{j} } \right) $$

(12)

$$ u_{j} = u_{j} + \mu \cdot \left( {\frac{{h_{ij} }}{{u_{i} }} - 1} \right) \cdot \left( {u_{i} - u_{j} } \right) $$

(13)

where μ is a constant parameter which amplitude controls the speed of the dynamics. If h_ij < u_i, there is no influence of agent i and agent j.