We consider selfish sources that send updates to a monitor over a shared wireless access. The sources would like to minimize the age of their information at the monitor. Our goal is to devise strategies that incentivize such sources to use the shared spectrum cooperatively. Earlier work has modeled such a setting using a non-cooperative one-shot game, played over a single access slot, and has shown that under certain access settings the dominant strategy of each source is to transmit in any slot, resulting in packet collisions between the sources' transmissions and causing all of them to be decoded in error at the monitor. We capture the interaction of the sources over an infinitely many medium access slots using infinitely repeated games. We investigate strategies that enable cooperation resulting in an efficient use of the wireless access, while disincentivizing any source from unilaterally deviating from the strategy. Formally, we are interested in strategies that are a subgame perfect Nash equilibrium (SPNE). We begin by investigating the properties of the one-stage (slot) optimal and access-fair correlated strategies. We then consider their many-slot variants, the age-fair and access-fair strategies, in the infinitely repeated game model. We prove that the access-fair and age-fair strategies are SPNEs for when collision slots are longer than successful transmission slots. Otherwise, neither is a SPNE. We end with simulations that shed light on a possible SPNE for the latter case.

We investigate the coexistence of an age optimizing network (AON) and a throughput optimizing network (TON) that share a common spectrum band. We consider two modes of long run coexistence: (a) networks compete with each other for spectrum access, causing them to interfere and (b) networks cooperate to achieve non-interfering access. To model competition, we define a non-cooperative stage game parameterized by the average age of the AON at the beginning of the stage, derive its mixed strategy Nash equilibrium (MSNE), and analyze the evolution of age and throughput over an infinitely repeated game in which each network plays the MSNE at every stage. Cooperation uses a coordination device that performs a coin toss during each stage to select the network that must access the medium. Networks use the grim trigger punishment strategy, reverting to playing the MSNE every stage forever if the other disobeys the device. We determine if there exists a subgame perfect equilibrium, i.e., the networks obey the device forever as they find cooperation beneficial. We show that networks choose to cooperate only when they consist of a sufficiently small number of nodes, otherwise they prefer to disobey the device and compete.

Real-time monitoring applications have Internet-of- Things (IoT) devices sense and communicate information (status updates) to a monitoring facility. Such applications desire the status updates available at the monitor to be fresh and would like to minimize the age of delivered updates. Networks of such devices may share wireless spectrum with WiFi networks. Often, they use a CSMA/CA based medium access similar to WiFi. However, unlike them, a WiFi network would like to provide high throughputs for its users.We model the coexistence of such networks as a repeated game with two players, an age optimizing network (AON) and a throughput optimizing network (TON), where an AON aims to minimize the age of updates and a TON seeks to maximize throughput. We define the stage game, parameterized by the average age of the AON at the beginning of the stage, and derive its mixed strategy Nash equilibrium (MSNE). We study the evolution of the equilibrium strategies over time, when players play the MSNE in each stage, and the resulting average discounted payoffs of the networks. It turns out that it is more favorable for a TON to share spectrum with an AON in comparison to sharing with another TON. The key to this lies in the equilibrium strategy of the AON that occasionally refrains all its nodes from transmitting during a stage. Such stages allow the TON competition free access to the medium.