εἴ ποτέ τοι πολύμητις ἐνὶ μεγάροισιν Ὀδυσσεὺς
ἢ βοὸς ἢ ὄϊος κατὰ πίονα μηρία κῆε,
τῶν νῦν μοι μνῆσαι καί μοι φίλον υἷα σάωσον,
μνηστῆρας δ’ ἀπάλαλκε κακῶς ὑπερηνορέοντας.
if ever Odysseus of many wiles in his palace
burnt for you the fat thigh pieces of either a heifer or a ewe,
remember them for me now and save my dear son for me,
and ward off the overbearing suitors.
In an appeal to a god, the earlier favor is usually a sacrifice, as here. In inter-human relationships, we find references to earlier hospitality or kept promises, as with Telemakhos’ appeal to Nestor for information about his father:
ἢ ἔπος ἠέ τι ἔργον ὑποστὰς ἐξετέλεσσε
δήμῳ ἔνι Τρώων, ὅθι πάσχετε πήματ’ Ἀχαιοί·
τῶν νῦν μοι μνῆσαι, καί μοι νημερτὲς ἐνίσπες.
promised you something, either by word or by deed, and kept it
in the land of Trojans, when you Achaeans suffered calamities;
remember them for me now, and tell me the truth.
The formula asking for remembering and the reciprocating action is the same in the case both of Penelope and of Telemakhos — τῶν νῦν μοι μνῆσαι, καί μοι, “remember them for me now, and [do something] for me” — and so, the linking of memory with returning favors as is fitting appears to be traditional. 
ἡρώων, ὅτε κέν τιν’ ἐπιζάφελος χόλος ἵκοι·
δωρητοί τε πέλοντο παράρρητοί τ’ ἐπέεσσι.
μέμνημαι τόδε ἔργον ἐγὼ πάλαι, οὔ τι νέον γε,
ὡς ἦν· ἐν δ’ ὑμῖν ἐρέω πάντεσσι φίλοισι.
whenever violent wrath would come to one of them:
they were both open to gifts and persuaded by words.
I remember this deed of old, indeed nothing new,
how it happened: and I will tell it among you, all dear close friends.
After this introduction, Phoinix launches into the story of Meleager’s anger and how he is eventually appeased and joins battle, as an example for Achilles to follow, even spelling out what he wishes Achilles to do as he concludes the story (Iliad 9.600–605). This is in structure very similar to, if much longer and more elaborate than, the examples of supplication of a god, a friend, or a guest/host, in terms of remembering or reminding about some relevant past action and asking for a specific action in return for it in the present time. The only difference is that the earlier, personal, favor that should now be returned is here replaced by a mythological exemplum. While appropriate reciprocation is part of the scene between Achilles and the embassy, the argument from memory for Achilles to adopt a specific course of action does not hinge on returning a favor — memory can be employed to elicit appropriate behavior without referring to reciprocation, as well.
μή τις ἔτι πρόφρων ἀγανὸς καὶ ἤπιος ἔστω
σκηπτοῦχος βασιλεύς, μηδὲ φρεσὶν αἴσιμα εἰδώς,
ἀλλ’ αἰεὶ χαλεπός τ’ εἴη καὶ αἴσυλα ῥέζοι,
ὡς οὔ τις μέμνηται Ὀδυσσῆος θείοιο
λαῶν, οἷσιν ἄνασσε, πατὴρ δ’ ὣς ἤπιος ἦεν.
ἀλλ’ ἦ τοι μνηστῆρας ἀγήνορας οὔ τι μεγαίρω
ἕρδειν ἔργα βίαια κακορραφίῃσι νόοιο·
σφὰς γὰρ παρθέμενοι κεφαλὰς κατέδουσι βιαίως
οἶκον Ὀδυσσῆος, τὸν δ’ οὐκέτι φασὶ νέεσθαι.
νῦν δ’ ἄλλῳ δήμῳ νεμεσίζομαι, οἷον ἅπαντες
ἧσθ’ ἄνεω, ἀτὰρ οὔ τι καθαπτόμενοι ἐπέεσσι
παύρους μνηστῆρας κατερύκετε πολλοὶ ἐόντες.
May no king that holds the sceptre still have a gracious mind,
be gentle and kind, and may he not know what is fitting in his mind,
but may he always both be harsh and work evil,
since not one remembers divine Odysseus
of the people whom he rules, and how kind a father he was.
But in truth, let me tell you, I do not grudge the arrogant suitors
their doing violent deeds in the mischievousness of their minds;
for staking their own heads they violently eat up
the house of Odysseus, and say that he will no longer come back.
But now I am wroth with the rest of the people — how you all
sit in silence, but, accosting them with words,
you do not hold back the few suitors although you are more numerous.
There is in Mentor’s words an implication of what would be the appropriate reciprocation in relationships between subjects and their just kings, similar to what we have seen between suppliants and their patrons, and guests and their hosts. Again, the principle necessary for maintaining the appropriate relationship is memory — οὔ τις μέμνηται Ὀδυσσῆος θείοιο / λαῶν, οἷσιν ἄνασσε, πατὴρ δ’ ὣς ἤπιος ἦεν, “not one remembers divine Odysseus of the people whom he rules, and how kind a father he was” (Odyssey 2.33–34) — if he and his kindness were remembered, the current state of affairs would not obtain.  Moreover, Mentor’s name signifies ‘he who reminds’ — perhaps why it is unnecessary for him to tell his listeners to remember, with anything he says automatically being a reminder. 
οἶκος ἐμὸς διόλωλε· νεμεσσήθητε καὶ αὐτοί,
ἄλλους τ’ αἰδέσθητε περικτίονας ἀνθρώπους,
οἳ περιναιετάουσι· θεῶν δ’ ὑποδείσατε μῆνιν,
μή τι μεταστρέψωσιν ἀγασσάμενοι κακὰ ἔργα.
λίσσομαι ἠμὲν Ζηνὸς Ὀλυμπίου ἠδὲ Θέμιστος,
ἥ τ’ ἀνδρῶν ἀγορὰς ἠμὲν λύει ἠδὲ καθίζει·
in which my house has been utterly destroyed: you yourselves should resent it,
and be ashamed before the other neighboring men,
who live around here; fear the mēnis of the gods,
lest angry at evil deeds they turn things round into punishment.
I beseech both the Olympian Zeus and Themis,
who dissolves and seats the assemblies of men.
Leonard Muellner has well demonstrated the significance of this part in Telemakhos’ speech in its connection to the theme of mēnis. This term is often translated as ‘wrath’, but he argues that it refers not to an emotion, but to “a sanction meant to guarantee and maintain the integrity of the world order,” “a social force whose activations brings drastic consequences on the whole community.”  The incurrence of mēnis “implies the prohibited transgression of fundamental cosmic rules,” among which are those of reciprocity and hospitality.  mēnis enforces the sovereign cosmic order, whether maintaining the social and political coherence of the divine community or the hierarchical distinctions between men and gods, or among men. Indeed, Muellner notes the continuity of human social hierarchy with that of the world as a whole, and the consequent lack of distinction between upholding the world order and the moral balance of human society — such that many human interactions, including those to do with reciprocal exchange, may incur mēnis when conducted incorrectly.  He also notes that as continuity is crucial to maintaining the world order, solidarity, on which this continuity depends, becomes important; thus an offence of an individual results in mēnis against not only that individual but the entire social group to which he belongs.  Muellner comments on this section of Telemakhos’ speech with the following:
In Telemakhos’ speech we have, firstly, mēnis indicating a punishment for bad behavior — and fear of it as guiding one to the right path. Secondly, we have an illustration of the role of solidarity in upholding the desired state of affairs, and hence the extension of the sense of outrage and consequent punishment from the offenders proper to their social group (Odyssey 2.63–69).
Ἀργείοισ’, ἐπεὶ οὔ τι νοήμονες οὐδὲ δίκαιοι
πάντες ἔσαν· τῶ σφεων πολέες κακὸν οἶτον ἐπέσπον
μήνιος ἐξ ὀλοῆς γλαυκώπιδος ὀβριμοπάτρης.
for the Argives, since not all of them were intelligent 
or just: therefore many of them met evil doom
on account of the destructive mēnis of the gleaming-eyed daughter of
a mighty father.
mēnis is here provoked by actions and a state of mind that betray a lack of noos, as well as injustice (οὔ τι νοήμονες οὐδὲ δίκαιοι, “not intelligent nor just,” Odyssey 3.233), just as in the case of Ares what is lacking is intelligence and concern for social constraints in the form of attention to aidōs, ‘sense of shame’, ‘respect’, and themis, ‘law established by custom’, ‘right’. themis, in fact, denotes the rules that enforce cosmic hierarchy and proper social behavior, and they are of divine origin.  As such, then, mēnis is an appropriate response to upsetting themis. Conversely, good phrenes are given as the explanation of proper conduct, for instance, in Eumaios’ unfailing appropriate behavior in the Odyssey: οὐδὲ συβώτης / λήθετ’ ἄρ’ ἀθανάτων· φρεσὶ γὰρ κέχρητ’ ἀγαθῇσιν, “nor did the swineherd forget the immortals: for he had good phrenes” (Odyssey 14.420–421), and so he makes an offering to the gods as a part of his preparation of the meal. Likewise, Mentor maintains as fair that in return for Odysseus’ people’s not remembering their king μή τις ἔτι πρόφρων ἀγανὸς καὶ ἤπιος ἔστω / σκηπτοῦχος βασιλεύς, μηδὲ φρεσὶν αἴσιμα εἰδώς, “may no king that holds the sceptre still have a gracious mind, be gentle and kind, and may he not know what is fitting in his mind” (Odyssey 2.230–231). πρόφρων, “with forward mind,” “with gracious mind,” and φρεσὶν αἴσιμα εἰδώς, “knowing what is fitting in his mind,” here both contain the element phrenes. Bad, or no, memory calls for reciprocation that shows an equally poor mind.
τείρεσθ’, εἰ μή πού τι πατὴρ ἐμὸς ἐσθλὸς Ὀδυσσεὺς
δυσμενέων κάκ’ ἔρεξεν ἐϋκνήμιδας Ἀχαιούς,
τῶν μ’ ἀποτεινύμενοι κακὰ ῥέζετε δυσμενέοντες,
τούτους ὀτρύνοντες. ἐμοὶ δέ κε κέρδιον εἴη
ὑμέας ἐσθέμεναι κειμήλιά τε πρόβασίν τε·
εἴ χ’ ὑμεῖς γε φάγοιτε, τάχ’ ἄν ποτε καὶ τίσις εἴη·
τόφρα γὰρ ἂν κατὰ ἄστυ ποτιπτυσσοίμεθα μύθῳ
χρήματ’ ἀπαιτίζοντες, ἕως κ’ ἀπὸ πάντα δοθείη·
νῦν δέ μοι ἀπρήκτους ὀδύνας ἐμβάλλετε θυμῷ.
unless my father good Odysseus,
bearing ill-will, did evil deeds against the well-greaved Achaeans,
avenging which you are doing evil deeds to me, bearing ill-will,
by encouraging these men [the suitors]. And it would be more profitable for me
to have you eat up both my possessions and live-stock;
if indeed it was you who ate, then recompense would be quick:
for up and down the town we would be greeted warmly by speech,
demanding back our belongings, until everything were given back;
but now you throw incurable distress in my heart.
His speech makes it clear that the suitors’ feasting at Odysseus’ house is a matter that, when properly conducted, calls for an appropriate reciprocal return.  Further, Telemakhos asserts that the fact of the suitors’ outrageous behavior — and the Ithacans’ not stopping it — would be explicable as a return for earlier bad conduct on his father’s part. Here even the phrasing shows the careful reciprocal balance with a chiastic ordering of the repeated words: δυσμενέων κάκ’ ἔρεξεν ἐϋκνήμιδας Ἀχαιούς, / τῶν μ’ ἀποτεινύμενοι κακὰ ῥέζετε δυσμενέοντες, “[unless Odysseus,] bearing ill-will, did evil deeds against the well-greaved Achaeans, avenging which you are doing evil deeds to me, bearing ill-will” (Odyssey 2.72–73). Reciprocating both good turns and bad is the norm. And so, as Telemakhos has said earlier in his speech, if the suitors’ bad conduct and the Ithacans’ passivity are not a return for an earlier evil, then it is properly reciprocated by the mēnis of the gods. Mentor, in his speech echoing Telemakhos’, echoes these ideas as well, but he is clear on the point of Odysseus’ record as a good ruler and that these evil deeds taking place in Ithaca are not an appropriate return for it. According to him, the suitors are preparing to repay their abuse of Odysseus’ house and livelihood with their lives (σφὰς γὰρ παρθέμενοι κεφαλὰς, “for staking their own heads,” Odyssey 2.237), but the Ithacans, who do not remember the kindliness of Odysseus, deserve a different reciprocation, namely, a harsh ruler. Just as in Telemakhos’ speech mēnis is entangled in the network of reciprocal exchanges, so in Mentor’s is memory.
The name for this kind of a rule is themis, which, as noted above, is often at stake or imperiled in episodes involving mēnis.  themistes (plural of themis) maintain proper social behavior while enforcing the cosmic hierarchy, and personified as a goddess, Themis is the guardian of social order, a role of which we have an indication in the passage from Telemakhos’ speech in the assembly, Odyssey 2.63–69 (quoted above). In governing the rules of exchange value, themistes are also involved in reciprocal exchange.  As Marcel Mauss notes in his study of the organization of contractual law and the system of the economic services of archaic and “so-called primitive societies,” these systems of exchange simultaneously express all aspects of the social life of that society:
Reciprocal exchange in the Homeric society cannot be isolated from other aspects of that society without losing a facet of its meaning — it is also an articulation of the social order, of the cosmic hierarchy, an instance of the working of themis.  Reciprocity, therefore, carries also moral connotations.
μή μ’ ἄκλαυτον ἄθαπτον ἰὼν ὄπιθεν καταλείπειν
νοσφισθείς, μή τοί τι θεῶν μήνιμα γένωμαι
Do not leave me behind unwept and unburied as you go,
turning your back on me, lest I become a mēnima [‘cause for mēnis’] of the gods
According to Watkins, the reciprocity demonstrated here is that it is the humans’ part to remember, be mindful of (μνήσασθαι, “to remember,” Odyssey 11.71) the divinely imposed order, here specifically the rites due to the dead, and the part of the gods is to provide mēnis, here manifested as mēnima, ‘cause for mēnis’, of the gods, as a deterrent against or a punishment for violating this order. 
ἔργον ἀντ’ ἀγαθõν | μνᾶμ’ ἀνέθεκε τόδε
There is, here, mnāma (= mnēma), a ‘memory’, ‘memorial’, ‘monument’, from the part of the human for the god, as there should be in the relationship between gods and men according to Watkins, too. What the god has given him, however, is fulfillment of his prayer, ergon agathon, ‘a good deed’ — no mēnis, which is antithetical to good deeds. mēnis, on the contrary, is a reaction to — reciprocates — kaka erga, ‘evil deeds’, in Odyssey 2.66–67, and in Odyssey 3.132–135 kakos oitos, ‘evil doom’, is a manifestation of mēnis (both passages are discussed above). Inscriptions of this votive type present a relationship of reciprocating good turns rather than one of memory on one hand and mēnis on the other.  The way the reciprocal relationship is articulated in this passage presents us with what we may call the ideal situation: both sides are doing good turns for each other, and there is memory, explicitly given by the human side to the divine. But once given, the dedicated object, the mnāma, can also function as a reminder for the divine side — and so there is memory on both sides, as well as good turns. Therefore, refining further the asymmetry in the reciprocal relationship between mēnis and memory, it is really memory that reciprocates memory (and concomitant good turn), while mēnis is a return for hubris, or, as Gregory Nagy points out with reference to Iliad 1.247, there can be mēnis on both sides.  Some dedications show that this order of a favor from a god and its return from a human can be reversed, too: in contrast to the one above, these dedications declare themselves to be the first part of the exchange, and ask for a reciprocating favor from the god. We have one such situation described in the inscription on the Mantiklos Apollo (CEG 326) with its request for χαρίϝετταν ἀμοιβ[άν], “gracious” or “graceful requital” in return for the statuette, the mnāma in this case.  Other dedications go even further and express a wish for a continuing cycle of favors and their reciprocation between the human and the god in question, as with Telesinos Ketios’ dedication of an image on the acropolis, which asks the goddess to take pleasure in it (χαίροσα) and to allow Telesinos to dedicate another (CEG 227 = IG I3 728). 
ὑμετέρων τὸ πρόσθεν ἀκούετε, παῖδες ἐόντες,
οἷος Ὀδυσσεὺς ἔσκε μεθ’ ὑμετέροισι τοκεῦσιν,
οὔτε τινὰ ῥέξας ἐξαίσιον οὔτε τι εἰπὼν
ἐν δήμῳ; ἥ τ’ ἐστὶ δίκη θείων βασιλήων·
ἄλλον κ’ ἐχθαίρῃσι βροτῶν, ἄλλον κε φιλοίη.
κεῖνος δ’ οὔ ποτε πάμπαν ἀτάσθαλον ἄνδρα ἐώργει·
ἀλλ’ ὁ μὲν ὑμέτερος θυμὸς καὶ ἀεικέα ἔργα
φαίνεται, οὐδέ τίς ἐστι χάρις μετόπισθ’ εὐεργέων.
to your fathers telling of the past when you were children,
what kind of a man Odysseus was among your parents,
doing nothing or saying nothing lawless
in the land? And this is the custom of divine kings:
he may hate one mortal and love another.
But he [Odysseus] never at all treated a man wickedly:
but your mind and unseemly deeds
are plain to see, and there is no kharis afterwards for good deeds.
Penelope here echoes the sentiment expressed by Mentor in Odyssey 2, that it is ignorance or forgetfulness of Odysseus’ kindness as a ruler that explains the suitors’ arrogance. ἀκούετε (Odyssey 4.688), “you (pl.) hear,” here corresponds to a function of mimnēskomai, ‘remember’, namely, when the latter denotes the performance of klea andrōn, epic songs about the glory of men: as mimnēskomai marks the activity of the bard, akouō, ‘hear’, is what the audience would do.  The applicability of this constellation of concepts to the present passage is supported by Penelope’s insistence that Odysseus’ actions in the past were not only praiseworthy, but in fact also the subject of discourse — we can picture the suitors’ parents performing klea andrōn, specifically the kleos of Odysseus. From another perspective, it could be added that she implies that lēthē is in action here: if the parents of the suitors did tell stories of Odysseus but the suitors’ behavior does not manifest any awareness of his good conduct in the past, these stories lanthanousi them — escape their notice — or the suitors lanthanontai, ‘forget’, them. This approach, too, draws a contrast with memory, and correlates poor conduct with forgetfulness. Memory, or more precisely, as with Mentor’s speech, a lack of it is assumed to lie behind the suitors’ inappropriate conduct here. Further, Penelope spells out that their behavior is no fitting return for Odysseus’ treatment of his fellow men, and that the appropriate kind of reciprocation is manifestly not to be had (4.693–695).  In this, too, she echoes Mentor as well as Telemakhos, though she articulates the ideas involved with slightly different vocabulary: she uses the term kharis.
ἄνδρα τε καὶ οἶκον, καὶ ὁμοφροσύνην ὀπάσειαν
ἐσθλήν· οὐ μὲν γὰρ τοῦ γε κρεῖσσον καὶ ἄρειον,
ἢ ὅθ’ ὁμοφρονέοντε νοήμασιν οἶκον ἔχητον
ἀνὴρ ἠδὲ γυνή· πόλλ’ ἄλγεα δυσμενέεσσι,
χάρματα δ’ εὐμενέτῃσι· μάλιστα δέ τ’ ἔκλυον αὐτοί.
a husband and a home, and may they grant you besides good
unity of mind and feeling: for there is nothing stronger and better,
than when, thinking alike in their minds, husband and wife
have their home; many a grief for their enemies,
and source of joy [kharmata] for their well-wishers; but they perceive it best
This ideal marriage that Odysseus paints for Nausikaa is characterized most prominently by likemindedness, which is even mentioned twice in the passage (ὁμοφροσύνην, “unity of mind and feeling,” “likemindedness,” Odyssey 6.181; ὁμοφρονέοντε, “thinking alike,” “being likeminded,” “being of one mind,” Odyssey 6.183) and singled out as the greatest good for a married couple. Furthermore, the likemindedness of the couple is a source of algea, ‘grief’, for their enemies (Odyssey 6.184). Odysseus’ words resonate with his own experience and the overall plot of the Odyssey, as we see the algea for the enemies of the likeminded couple played out in the poem when the likemindedness of Odysseus and Penelope causes grief indeed to the suitors and their families.  In contrast, this likemindedness of the good couple brings many kharmata, many a source of joy, to their well-wishers (Odyssey 6.184–185). kharma (singular of kharmata), ‘source of joy’, ‘delight’, is connected to khairō, ‘take pleasure’, ‘rejoice’, and kharis, so here, too, we can perceive in the ideal this graceful element.  In addition, Odysseus says that the couple ἔκλυον, “perceive” (Odyssey 6.185), this highest good best themselves. kluō, ‘hear’, ‘perceive’, is itself connected to kleos, ‘song of glory’, and so, not only does the likemindedness of the couple bring kharis to those on their side, in their solidarity group, but there is here even a suggestion of its ability to generate kleos for the couple themselves. 
ἦ ἄρα σὺν μεγάλῃ ἀρετῇ ἐκτήσω ἄκοιτιν·
ὡς ἀγαθαὶ φρένες ἦσαν ἀμύμονι Πηνελοπείῃ,
κούρῃ Ἰκαρίου, ὡς εὖ μέμνητ’ Ὀδυσῆος,
ἀνδρὸς κουριδίου. τῶ οἱ κλέος οὔ ποτ’ ὀλεῖται
ἧς ἀρετῆς, τεύξουσι δ’ ἐπιχθονίοισιν ἀοιδὴν
ἀθάνατοι χαρίεσσαν ἐχέφρονι Πηνελοπείῃ.
in truth then with great excellence you acquired your wife:
how good was the mind [phrenes] of blameless Penelope,
daughter of Ikarios, how well she remembered [memnēt’] Odysseus,
her wedded husband. Therefore the song of glory [kleos] of her excellence 
will never perish, and the immortals will make a kharis-filled song
for the mortals in honor of the sensible [having phrenes] Penelope. 
While Odysseus’ words to Nausikaa intimate that likemindedness is extolled as worthy of kleos, Agamemnon’s praise emphatically confirms this and make this source of kleos in the Odyssey explicit. It is the mind of Penelope and her remembering Odysseus that is worthy of celebration — and it is, again, a much-contriving Odysseus, his epithet pointing to his mental abilities, who has the luck of having Penelope as his wife. Further, this passage shows the connection between the worthy achievements and their commemoration in song very clearly. Agamemnon speaks specifically of song and reputation conveyed through it. Moreover, the good person’s praise poetry in Agamemnon’s exclamation is characterized by kharis: the kleos is an aoidē khariessa, a ‘kharis-filled song’ (Odyssey 24.197–198), just as the likemindedness of the couple in Odysseus’ wishes for Nausikaa is the cause of kharmata, ‘source of joy’ (Odyssey 24.185), for their well-wishers. And here we have one such well-wisher, Agamemnon, exclaiming on the happiness of Odysseus and Penelope, and even calling their kleos kharis-filled himself.